Experimental Skills

Experimental skills are essential for understanding and applying scientific concepts in real-world contexts. They allow individuals to investigate problems, test hypotheses, and draw evidence-based conclusions. These skills foster critical thinking, accuracy, and creativity, which are crucial in both academic research and practical applications. Developing strong experimental abilities also enhances problem-solving, supports innovation, and prepares learners for future scientific or technical careers.

Exploring Experimental skills using Vernier Calipers, Screw Gauge, Simple Pendulum, Metre Scale, and concepts like Young's Modulus, Surface Tension, Co-efficient of Viscosity, Speed of Sound, Specific Heat Capacity, and Resistivity. Master Ohm’s Law, Galvanometer, Convex & Concave Mirrors, Convex Lens, Angle of Deviation, Travelling Microscope, and identification of Diodes, LEDs, Resistors, Capacitors, and Zener Diode essential for JEE and NEET Exam preparation.

1.0Vernier calipers

It is a device, designed by a French Mathematician Pierre Vernier to measure accurately upto $(\frac{1}{10}{)}^{th}$ of a millimetre. It has four parts :-

1. Main scale :It is a steel metallic strip M with fixed jaws as shown in figure, graduated in cm and mm on one edge and inches on the other side which is not shown in the figure.
2. Jaws (internal and external):It has two fixed jaws A and C and two movable jaws B and D as shown in the figure. Jaws A and B are to measure thickness or length and C & D to measure internal diameter of vessel. When jaws A and B are closed, the straight parts of C and D jaws also touch each other.
3. Vernier scale: Vernier scale slides freely left or right on metallic strip M. It can not only slide but also be fixed in any position by screw S. In laboratory vernier calipers, the vernier scale has 10 divisions which coincide with 9 mm of the main scale.

Note : In questions it is not necessary that 9 main scale divisions coincide with 10 vernier scale divisions you will get information about this in question.

4. Metallic strip: A metalstrip E attached to the back side of M and connected with vernier scale. When jaws A and B touch each other, the edge of E touches the edge M. The strip E is used for measuring depth of vessels.

Vernier Constant or Least count : The difference between one main scale division (MSD) and one vernier scale division (VSD).

V.C.=1MSD-1 VSD

Now suppose the size of one main scale division is M units and that of one vernier scale division is V units. Also suppose that the length interval of b vernier divisions is equal to the length interval of a main scale division.

$aM=bV\Rightarrow V=\frac{a}{b}M$

V.C or L.C.= $M-V=M-\frac{a}{b}M=(\frac{b-a}{b})M$

2.0Zero Error and its Types

Due to wear and tear of the jaws by some manufacturing defect, the zero marks of the main scale and vernier scale may not be in the same straight line, when the jaws A & B are made to touch each other. This error is known as zero error. It can be positive or negative.

1. Positive error : The zero error is positive when the zero mark of the vernier scale lies towards the right side of the zero of the main scale (figure).

2. Negative error: When the zero mark of the vernier scale lies towards the left side of the zero of the main scale (figure), then the zero error is called negative error.

Correction of zero Error: To get the correct reading, zero error with proper sign is subtracted from the observed reading.

Means : Actual reading = observed reading – zero error

Observed Reading=MSR+(VSR) ✕ (L.C)

Correct reading = measured reading – zero error

Correct reading=MSR+(VSR) ✕ (L.C) - Zero Error

We use vernier calipers in which 10 VSD coincide with 9 MSD and the main scale has 10 divisions in 1 cm.

1MSD=$\frac{1}{10}$cm and N=10 (N=No. of VSD)

$V.C.=\frac{1MSD}{N}=\frac{1}{10}\times \frac{1}{10}cm$=0.01 cm=0.1mm

Example- A vernier scale contains 10 equal divisions. These 10 divisions (each of length V units) coincide with 9 equal divisions (each of the length S units) of the main scale. The length of one small division on the main scale is 1 mm, i.e., S = 1 mm, then calculate the vernier constant.

Solution:

10V=9S                        $\therefore (S-V)=S-\frac{9}{10}S$

$(S-V)=(1-\frac{9}{10})S=\frac{1}{10}S$      But S=1mm

$(S-V)=\frac{1}{10}mm$

$V.C=\frac{1}{10}mm=0.1mm=0.01cm$

3.0Screw Gauge

• A screw gauge is a precision instrument used to measure small lengths or thicknesses with high accuracy, typically up to 0.01 mm.
• When a screw rotates in a nut, it both spins and moves linearly along its axis. The distance it moves in one full rotation is called the pitch, equal to the space between two consecutive threads.

Least Count : For a screw, it is defined as the ratio of the pitch to the total number of divisions made on the circular cap/scale as shown in above figure.

$\text{Least Count}=\frac{Pitch}{Totalnumberofdivisiononthecircularscale}$

suppose the circular scale is divided into 100 equal parts and the pitch of the screw is 1mm, then

Least Count=$\frac{1mm}{100}=0.01mm$ or 0.001 cm or 10 m

Note: Due to its micrometer-level precision, a screw gauge is also called a micrometer screw. Both the micrometer and spherometer work on the screw principle.

• The screw gauge has a U-shaped gunmetal frame E for durability.
• One end has a stud (P) with a flat face; the other has a tubular hub (T) with internal threads.
• A screw (Q) moves inside the hub; its front face is also flat.
• The main scale (M), marked in mm, lies on the extended hub—called the pitch scale.
• A cylindrical cap attached to the screw can rotate freely, moving the screw in or out.
• The circular scale on the cap (divided into 50 or 100 parts) is used for fine measurements.
• A ratchet (R) prevents over-tightening and clicks when the faces P and Q meet.
• If the circular scale’s zero doesn't align with the main scale’s zero when closed, it has a zero error (positive or negative).
• Positive Zero Error: When the circular scale's zero does not cross the baseline of the main scale.
• Negative Zero Error: When the circular scale's zero crosses the baseline of the main scale.
• Backlash Error: Caused by loose fitting or worn threads; the screw may rotate without moving.

Note: Minimized by rotating in the same direction during measurements.

4.0Simple Pendulum

 Dissipation of energy by plotting a graph between square of amplitude and time for simple pendulum.

1. In undamped SHM, force on a pendulum is: F = –kx, where k = mg/L.
2. In ideal conditions, amplitude and energy stay constant.
3. In the real world, due to damping (e.g., friction), amplitude and energy decrease exponentially. Such oscillations are called damped oscillations.
4. Energy ∝ (amplitude)², so energy loss can be studied by plotting amplitude vs. time.

Parameters	Undamped oscillation	Damped oscillation
Amplitude	$A=A_O=Constant$	$A=A_o{e}^{-bt/2m}=A_o{e}^{-\lambda t}$ Note : Due to damping amplitude decreases exponentially with time and becomes zero after a very long time.
Total Energy(E)	$E_0=\frac{1}{2}K{A}_o^2$	$E=\frac{1}{2}K{A}^2=\frac{1}{2}K{\left[A_0{e}^{-bt/2m}\right]}^2$ $E=\left(\frac{1}{2}K{A}_0^2\right)e^{-bt/m}=\left(E_0\right)e^{-bt/m}=E_0{e}^{-(2\lambda )t}$ Note : Due to damping, energy decreases exponentially and becomes zero after a long time.

5.0Metre Scale

• If a beam or rod is balanced under the action of different forces, then about point of balance or equilibrium position : Sum of clockwise moments = Sum of anticlockwise moments.
•  The vector sum of moments of all forces is zero about a point at which the body is in equilibrium or in balanced position.
•  The vector sum of clockwise and anticlockwise moments is zero about an axis of rotation chosen. This principle is used in common balance to measure the mass of the body.

On applying the principle of moments, we have

$(mg)(x)=(mg)(y)\Rightarrow m=M(\frac{y}{x})$

Unknown mass m= mean of all calculated values

6.0Young's Modulus of Elasticity

Young's modulus is the ratio of stress to strain in a material within the elastic limit. It measures a material's stiffness.

$Y=\frac{Stress}{Strain}=\frac{F/A}{\Delta L/L}=\frac{FL}{A\Delta L}=N/m^2$or Pascals

Searle’s Apparatus: It is used to determine Young's modulus of elasticity of the material of a given wire.

• Wire A (reference) and Wire B (experimental) are fixed to frames $F_1$ and $F_2$.
• Weights  $W_{1}and{W}_2$  stretch Wire B via hooks $H_{1}and{H}_2$.
• Frames are connected by a hinged bar PQ, allowing only vertical motion.
• A spherometer with least count 0.01 mm is attached; tip R is fixed, C is adjustable.
• When Wire B stretches, $F_2$ and the spherometer moves down, shifting the spirit level bubble.
• To restore the bubble to its original position, screw C is adjusted.

If a wire of length L and cross-section A is stretched by an amount l by a force F acting along its length, then

$Stress=\frac{F}{A}$ and $Strain=\frac{l}{L}$

$\text{Young’s Modulus}=Y=\frac{F}{A}\times \frac{L}{l}$

Where F=Mg and $A=\pi r^2$

$Y=\frac{MgL}{\pi r^{2}l}$

7.0Surface Tension of water

• Determine the surface tension of water by capillary rise method.
• When a liquid rises in a capillary tube, whose one end is placed in the liquid, the weight of the column of liquid of density   below the meniscus, is supported by the upward force of surface tension acting around the circumference of point of contact. Therefore,

$2\pi rT=\pi r^{2}h\rho g$ (approx for water)

$T=\frac{h\rho gr}{2}$

Surface Tension (ST)

• It is the property of a liquid surface that acts like a stretched elastic membrane, trying to minimize surface area.
•  Surface tension is the force per unit length acting perpendicular to an imaginary line on the liquid surface.

Intermolecular forces

(a) Cohesive force : The force acting between the molecules of one type of molecules of the same substance is called cohesive force.

(b) Adhesive force : The force acting between different types of molecules or molecules of different substances is called adhesive force.

• Molecular Range: Distance up to which these forces are effective, ~10-9m
• Variation with Distance: Within the molecular range, force increases rapidly as distance decreases.
• Dependence: Depends on the nature of the substance.

Angle of Contact$({\theta }_c)$:The angle enclosed between the tangent plane at the liquid surface and the tangent plane at the solid surface at the point of contact inside the liquid is defined as the angle of contact.

8.0Capillary Tube and Capillarity

Capillarity is the tendency of a liquid to rise or fall in a narrow tube due to surface tension. This rise or fall is called capillary action.

Calculation of Capillary Rise

1. Pressure Balance Method: When a capillary tube is dipped in a liquid, the liquid rises to height h, forming a curved meniscus of radius R. Let r be the tube radius, T the surface tension, θ the contact angle, and ρ the liquid's density. By Pascal’s law, pressure at the same horizontal level (points A and B) is equal.

$P_A=P_B\Rightarrow P_A=P_C+\rho gh$

Now, point C is on the curved meniscus which has $P_{atm}$ and $P_c$ as the pressures on its concave and convex sides respectively.

$P_{\text{atm}}=\left(P_{\text{atm}}-\frac{2T}{R}\right)+h\rho g\Rightarrow h=\frac{2T}{R\rho g}=\frac{2T\cos {\theta }_c}{r\rho g}$

2. Force Balance Method :-The liquid continues to rise in the capillary tube until the weight of the liquid column becomes equal to force due to surface tension.

In equilibrium : force due to S.T = weight of rise liquid

$(2\pi r)Tcos{\theta }_c=mg$

$h=\frac{2TCcos{\theta }_c}{r\rho g}$

3. Zurin's Law :The height of rise of liquid in a capillary tube is inversely proportional to the radius of the capillary tube, if T,, and g are constant or rh=constant. It implies that liquid will rise more in capillary tubes of less radius and vice versa.

• If a capillary tube is dipped into a liquid and tilted at an angle   from vertical then the vertical height of the liquid column remains same whereas the length of liquid column in the capillary tube increases. $h=lcos\alpha \Rightarrow l=\frac{h}{cos\alpha }$

• The height 'h' is measured from the lowest point of the meniscus. However, there exists some liquid above this line also. If correction is applied then the formula will be $T=\frac{\rho rg[h+\frac{1}{3}r]}{2cos\theta }$

9.0Co-efficient of Viscosity

To determine the coefficient of viscosity of a given viscous liquid by measuring the terminal velocity of a given spherical body, using stokes law.

Viscosity: Viscosity is a fluid's resistance to the relative motion between its layers, also known as internal friction. The opposing force is called the viscous force.

Stokes Law: Stoke's Law states that the viscous force Fₓ on a small sphere of radius r moving with velocity v through a fluid of viscosity η is given by: F=6πηrv

Terminal Velocity: Terminal Velocity is the constant velocity a solid sphere attains while falling in a liquid, when the viscous force balances the force of gravity.

At terminal velocity, the net upward force (upthrust + viscous force) balances the downward force (weight of the body), resulting in no acceleration.

$\frac{4}{3}\pi r^3\sigma g+6\pi \eta rv=\frac{4}{3}\pi r^3\rho g$$\Rightarrow v_T=\frac{2r^2(\rho -\sigma )}{9\times g}\eta$

Note: Terminal velocity is directly proportional to the square of the radius of the sphere. Thus, plotting v vs r² for spheres of different sizes gives a straight line.

10.0Resonance Tube

Find the speed of sound in air at room temperature using a resonance tube by two resonance positions.

• A 100 cm long tube (AB), made of glass or brass, has a 2.5 cm internal diameter.
• The tube is fixed vertically on a board with a meter scale.
• The zero of the scale coincides with the upper end of the tube.
• The lower end is connected to a water reservoir via rubber tubing and a pinch cock.
• The water level in the tube is adjusted using an adjustable screw on the reservoir.
• Pinch cock controls the water flow, and levelling screws ensure the tube is vertical.

End correction: The end correction accounts for the antinode occurring slightly above the open end of the resonance tube. It is given by 0.3D or 0.6R, where D is the diameter and R is the radius of the tube.

Principle:- If $l_{1}and{l}_2$ are the lengths of the air columns for the first and the second positions of resonance respectively,

$l_1+x=\frac{\lambda }{4}$……..(1)

$l_2+x=\frac{3\lambda }{4}$……..(2)

x = end correction ;  $\lambda$= wavelength of the sound wave.

$l_2-l_1=\frac{\lambda }{2}\Rightarrow \lambda =2(l_2-l_1)\Rightarrow v=n\lambda$

where v and n are the velocity and frequency of the sound wave respectively.

$v=2n(l_2-l_1)$

The velocity at 0°C is given by, $v_o=(v_t-0.61\times t)m/s$ where $v_t$ is velocity at room temperature t°C.

end correction, $x=\frac{l_2-3l_1}{2}$

11.0Specific heat capacity

(A). Determine specific heat of a given solid (lead shots) by methods of mixture

Principle: Law of mixtures Heat gained by cold substance = Heat loss by hot substance(Assuming no heat loss to the atmosphere)

1. Add ~100g of lead shots and water into the hypsometer; insert thermometer TB so its bulb is surrounded by lead.
2. Place a hypsometer on wire gauze and heat it using a burner.
3. Weigh the empty calorimeter with stirrer and lid; note as m₁.
4. Cool water using ice to 5–7°C below room temperature, then fill 2/3 of the calorimeter. Wipe off any moisture and weigh; record as m₂.
5. Place calorimeter in the jacket, insert thermometer TA, ensuring the bulb is immersed but not touching the bottom. Record the initial temperature of water.
6. Monitor lead temperature in a hypsometer every 2 minutes. When it stays steady for 5 minutes, record it as θ₂.

$\text{Mass of calorimeter + stirrer + lid}=m_{1}g$.

$\text{Mass of calorimeter + lid + cold water}=m_{2}g.$

Temperature of cold water in calorimeter = ${\theta }_1^{o}C$

Steady temperature of solid in hypsometer by thermometer B = ${\theta }_2^{o}C$

Final, i.e., equilibrium temperature of the mixture ${\theta }_e^{o}C$.

Mass of calorimeter + stirrer + lid + water + solid =  $m_{3}g.$

Water equivalent of calorimeter + stirrer, W = m (Mass of calorimeter) $\times \frac{S_c}{S_w}$

Applying law of mixtures, keeping in view the conditions,

Heat lost = Heat gained

$({\theta }_2-{\theta }_e)$

$(m_3-m_2)\times S({\theta }_2-{\theta }_e)=(m_w+W)\times S_w({\theta }_e-{\theta }_1)$

$S=\frac{(m_w+W)({\theta }_e-{\theta }_1)S_w}{(m_3-m_2)({\theta }_2-{\theta }_e)}J/gm/℃$

(B).Determine the specific heat of a given liquid (kerosene or turpentine oil) by method of mixtures.

Principle: Law of mixtures Heat gained by cold substance = Heat loss by hot substance(Assuming no heat loss to the atmosphere)

1. Heat a metal piece tied with thread in boiling water for 15–20 minutes.
2. Weigh the empty calorimeter (m₁) and then with liquid + stirrer (m₂); record initial liquid temperature (θ₁).
3. Weigh the hot metal piece (m₃) and quickly transfer it into the calorimeter with the liquid.
4. Avoid splashing, wipe off extra water from the metal, and cover the calorimeter with a lid.
5. Stir well and record the final (equilibrium) temperature (θₑ).

Mass of calorimeter + stirrer, $m_{1}g$

Mass of calorimeter + stirrer + oil, $m_{2}g$

Temperature of oil in the calorimeter, ${\theta }_1°C$

Temperature of boiling water in the beaker, i.e.

temperature of metal piece ${\theta }_2=100°C$

Steady equilibrium temperature of mixture ${\theta }_e°C.$

Water equivalent of calorimeter,

$W=mass\times \frac{specificheatofmaterialofcalorimeter}{specificheatofwater}$

Mass of oil $m=m_2\times 0.095$ (for copper calorimeter)

Applying law of mixtures

$({\theta }_e-{\theta }_1)(W+m{S}_l)=m_3\times S\times (100-{\theta }_e)$

Specific heat of liquid, $S_l=\frac{m_{3}S(100-{\theta }_e)}{m({\theta }_e-{\theta }_1)}-\frac{W}{m}(Jg{m}^{-1}°C^{-1})$

12.0Metre Bridge

Resistivity of the material of a given wire using a meter bridge.

1. Set up the meter bridge and make tight connections.
2. Place RB in the right gap, unknown X in the left gap, and insert resistance R = 2Ω.
3. Use jockey to find null point (no deflection); record AB = l,BC = 100 – l
4. Swap positions: RB in left, X in right, repeat to find new l.
5. Remove and straighten the unknown wire; measure its length and diameter using a screw gauge.

Principle: Meter bridge is based on the principle of Wheat stone bridge.

Unknown resistance $X=R(\frac{l}{100-l})$

specific resistance of the material of the given wire, $\rho =\frac{XA}{l}=\frac{X(\pi r^2)}{L}$

where r  and L are the radius and length of the given wire respectively.

13.0Ohm's law

• Find resistance of wire using ohm's law
• According to Ohm's law, "the current flowing through a conductor is directly proportional to the potential difference applied across its ends provided the physical conditions (temperature, dimensions, pressure) of the conductor remain the same.

$V\propto IorV=RI\Rightarrow R=\frac{V}{I}$

1. Draw the circuit diagram as shown.
2. Note range, least count, and zero error of voltmeter and ammeter.
3. Insert plug in key K, set rheostat to minimum current position.
4. Gradually adjust rheostat to increase current; record ammeter and voltmeter readings.
5. Take a total of 10 readings at different current values.

Using the readings of voltmeter (V) and ammeter (I) draw a graph as straight line

best fitting all the points.

Slope of V–I curve $=\frac{\Delta V}{\Delta I}=tan\theta =R$

14.0Galvanometer by Half Deflection Method

(A). Resistance of galvanometer by half deflection method

When a high resistance R is applied in the circuit with $K_1$ closed and $K_2$ open, the galvanometer draws a current Ig and shows a deflection   such that

$I_g=\frac{E}{R+G}$

where E, is emf of the battery and G is resistance of the galvanometer.

Now $K_2$ is closed. Adjust the resistance in LRB such that galvanometer deflection becomes equal to $\frac{\theta }{2}$Now the galvanometer draws the current.

$I_g^{\prime }=\frac{IS}{G+S}=\frac{ES}{R(G+S)+GS}$      Where $I=\frac{E}{R+\frac{GS}{S}}$

$I_g^{\prime }=\frac{1}{2}{I}_g$

$\frac{ES}{R(G+S)+GS}=\frac{1}{2}\frac{E}{R+G}$

$G=\frac{RS}{R-S}$

Knowing R and S, G can be calculated.

Also if R >> S, S can be dropped in comparison to R and then G S .

(B). Figure of merit of galvanometer: It is defined as the current required per division of deflection in galvanometer. It is denoted by(k)

$k=\frac{I}{\theta }$ The circuit diagram for determining the figure of merit (k)of a galvanometer is shown in the figure. When a high resistance R is introduced in the circuit through HRB, a small current $I_g$ is drawn by it and it shows a deflection such that

$I_g=k\theta =\frac{E}{R+G}$

Figure of merit $(k)=\frac{I}{\theta }\times \frac{E}{R+G}$

Maximum current measured by galvanometer or full scale deflection current for galvanometer $I_g$ = Number of division on one side of galvanometer scale × figure of merit

$\frac{I}{\theta }=\frac{k}{E}R+\frac{k}{E}G$

Graph between I and R

15.0Parallax Method

Parallax

1. Parallax is the apparent shift in position of two objects at different distances when the eye is moved sideways.
2. A distant object appears to shift with the eye; a nearer object shifts opposite to eye movement.
3. Remove parallax by adjusting one object until both appear aligned from any eye position.
4. When there's no relative shift, parallax is said to be removed.
5. This "no parallax" method is commonly used to locate images formed by mirrors or lenses.

Optical Bench: An optical bench is a horizontal base with a meter scale and 3–4 sliding uprights. These uprights hold components like the lens, mirror, object, or image needle, and can move sideways to align all tips in the same vertical plane. Marked indices on each upright help in recording their positions on the scale.

Bench error : The variation between the real distance between the point object and the mirror's pole and the recorded distance calculated on the optical bench.

$\text{Bench error = Actual distance – Observed distance}$

(A) Find the value of v for different values of u in case of concave mirror and to find the focal length.

u = distance of the object from pole

v = distance of the image from pole

1. Mount the concave mirror so its principal axis is horizontal and parallel to the optical bench.
2. Align object and image needles with the mirror’s pole along a straight line.
3. Place the object needle between F and C; observe its real, inverted image beyond C.
4. Adjust the image needle to remove parallax with the mirror image.
5. Record positions of mirror, object, and image; repeat for five different object positions.

In this graph, at point Q $u=v=2f$ $OP=OR=2f$ $f=\frac{OP}{2}$ or $\frac{OR}{2}$

$f=\frac{1}{OA}=\frac{1}{OB}$

(B).Find the focal length of a convex mirror using a convex lens. 

1. Place lens (L) between object needle (O) and convex mirror (M).
2. Adjust positions until there is no parallax between O and its image I.
3. At this point, rays fall normally on the mirror, and MI = radius of curvature (r).
4. Remove the mirror, adjust a needle at I′ (image formed by lens only) to remove parallax.
5. Measure MI′ to get the radius of curvature, then find focal length: f = r/2.

The focal length of convex mirror, $f=\frac{r}{2}=\frac{M{I}^{\prime }}{2}$

(C). Find the values of v for different values of u in case of a convex lens and to find its focal length.

Focal length of a lens from lens formula, $f=\frac{uv}{v-u}$

1. Find rough focal length by focusing a distant object’s image on paper and measuring lens-to-image distance.
2. Mount lens and align object (AB) and image needle (CD) tips at lens center height on optical bench.
3. Mark one needle to distinguish it (e.g., chalk or paper flag).
4. Place the object beyond 2f, view the real inverted image, and adjust CD to remove parallax.
5. Record positions of lens, object, and image to find u and v.
6. Repeat for 5 different object positions between F and 2F or beyond 2F.

16.0Triangular Prism

Determine angle of minimum deviation for a given glass prism by plotting a graph between the angle of incidence and angle of deviation.

1. Draw a base line XY on white paper, mark normal points (O) and draw incident rays (PQ) at various angles (30°, 40°, 50°, 60°) using a protractor.
2. Place the prism on XY, trace its boundary, and fix pins P & Q on the incident ray. View from AC face, align and fix pins R & S on the emergent side, then mark all pin pricks.
3. Join RS and extend it back to meet extended PQ; this gives the emergent ray and allows measurement of angle of deviation (δ). Repeat for different angles.
4. To find the angle of prism A, draw points E, O, F on XY with equal spacing and draw verticals EG, OI, FH. Place the prism along OI and trace its boundary again.
5. Use pin reflections from faces AB and AC to trace reflected rays, construct triangle LPN, and measure angle ∠LPN = 2A, so A = ∠LPN / 2.

Graph between angles i and $\delta$ for various sets of values

17.0Travelling Microscope

It is a compound microscope fitted vertically on a vertical scale. It can be moved up and down. It consists of a vernier scale moving along the main scale. The reading is taken by combining the main scale and vernier scale reading.

• For determination of refractive index, by measuring real and apparent depth, a travelling microscope is used. If the reading microscope when focused on ink mark on white paper r1 reading when the slab is kept over r2 and the reading of image of lycopodium powder then real depth=$r_3-r_1$and apparent depth=$r_3-r_2$
• Therefore refractive index of the material $\mu =\frac{r_3-r_1}{r_3-r_2}$

1. Find least count of microscope = (1 M.S.D. – 1 V.S.D.) using scale divisions.
2. Set the microscope vertically; adjust using rack and pinion screw.
3. Focus on a cross mark on paper and note reading r₁.
4. Place a glass slab over the cross, refocus and note r₂ (apparent position).
5. Sprinkle powder on slab, focus again and note r₃. Then: Real depth = $r_3-r_1$; Apparent depth = $r_3-r_2$

18.0P-N Junction Diode

Characteristic Curve of P-N Junction Diode

1. Forward Bias: Current rises slowly at first, then increases sharply after knee voltage (cut-in voltage).
2. At knee voltage, barrier potential is removed, and diodes offer low resistance.
3. Reverse Bias: Very small, nearly constant reverse saturation current flows.
4. Diodes show high resistance in reverse bias.
5. At breakdown voltage $(V_B)$reverse current rises sharply due to avalanche breakdown.

19.0 Zener Diode

Characteristic curve of a Zener diode and to determine its reverse breakdown voltage.

A Zener diode is a special diode designed to operate in reverse bias beyond the breakdown voltage $(V_Z)$. After $V_Z$, a small change in voltage causes a large change in current, but the voltage stays nearly constant, making it ideal for voltage regulation.

$V_I$= Input voltage, $V_o$ = Output voltage, $R_I$ = Input resistance, $R_L$ = Load resistance

$I_I$ = Input current, $I_Z$ = Zener diode current, $I_L$ = Load current

$I_L=I_I-I_Z$

$V_o=V_I-R_I{I}_I$

$V_o=I_Z{R}_L$

Initially as $V_I$ is increased, $I_I$ increases a little, then $V_o$ increases. At breakdown, increase of $V_I$  increases $I_I$  by large amount, so that $V_o=V_I-R_I{I}_I$ becomes constant. This constant value of $V_o$  which is the reverse breakdown voltage is called Zener voltage.

20.0Identification of Components( Diode, LED, Resistor,  Capacitor)

(A) Diode

A diode is a two-terminal device that conducts in forward bias and blocks current in reverse bias.

• The silver ring or flat side indicates the n-side, the other is the p-side.
• The arrow symbol shows current flow: from p to n.
• Diodes don’t emit light while conducting.
• In testing, if a multimeter shows deflection in one direction only, it’s a diode.

(B) Light emitting diode

An LED is a two-terminal device that conducts and emits light in forward bias, but does not conduct in reverse bias.

• Long pin = p-side, short pin = n-side.
• If a multimeter shows deflection with light in one direction and none in the other, the component is an LED.

(C) Resistor

A resistor is a two-terminal device that conducts equally in both directions.

• Identified by 3 color bands + gold/silver band.
• If a multimeter shows equal deflection both ways, it's a resistor.
• Color code:
  1st band = 1st digit
  2nd band = 2nd digit
  3rd band = multiplier
• Black –0, Brown –1, Red –2, Orange –3, Yellow –4, Green –5, Blue –6 ,Violet –7, Grey –8, White –9
• Tip: Use "BBROY GB VGW" to remember color order.

Resistance of the given resistor

$=27\times 10^3\pm 10\%of27\times 10^3$

$=(27\pm 2.7)10^3\Omega$

(D) Capacitor

1. A capacitor is a device that stores electric charge.
2. It blocks DC but allows AC to pass.
3. Common types of capacitors based on dielectric:

• Air capacitor – variable (e.g., gang capacitors)
• Mica capacitor – low capacitance
• Ceramic capacitor – very low capacitance
• Paper capacitor – low capacitance
• Plastic capacitor – general use
• Electrolytic capacitor – medium capacitance
• Oil-filled capacitor – high capacitance

Note: A capacitor is a two-terminal device that does not conduct DC but stores charge. In a multimeter test, it shows no deflection, or a brief deflection if capacitance is high.