Home
Class 12
PHYSICS
Two identical monochromaticlight sources...

Two identical monochromaticlight sources A & B intensity `10^(-15)W//m^(2)` produce wavelength of light `4000sqrt(3)Å` A glass of thickness 3mm is placed in the path of the ray as shown in figure the glass has a varible refractive index `n=1+sqrt(x)` where x (in mm) is distance of plate from left to right calculate total intensity at focal points F of the lens.

Text Solution

Verified by Experts

The correct Answer is:
`4xx10^(-15)W//m^(2)`
`I=10^(-15)W//m^(2),lamda=4000sqrt(3)Å,t=3mm`
The path difference due to glass plate 3mm. ltbr. Path difference `=intds=int_(0)^(3mm)(n-1)dx`
`int_(0)^(3)(1+sqrt(x)-1)dx=(2)/(3)x^(3//2)=2sqrt(3)mm`
`therefore` Phase difference
`=(2pi)/(4000sqrt(3)xx10^(-10))xx2sqrt(3)xx10^(-3)=pixx10^(7-3)`
`therefore2pin=10^(4)xxpi`
At point I there is point of maxima `n=5xx10^(3)`
`therefore` intensity `=I+I+2sqrt(I)xxsqrt(I)cos10^(4)pi`
`=4I=4xx10^(-15)W//m^(2)`
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • WAVE OPTICS

    ALLEN |Exercise Exercise 5 A (Previous Years Questions)|17 Videos

  • WAVE OPTICS

    ALLEN |Exercise Exercise 5 B (Previous Years Questions)|19 Videos

  • WAVE OPTICS

    ALLEN |Exercise Exercise 4 A (Conceptual subjective Exercise)|9 Videos

  • UNIT & DIMENSIONS, BASIC MATHS AND VECTOR

    ALLEN |Exercise Exercise (J-A)|7 Videos

Similar Questions

Explore conceptually related problems

A glass sheet 12xx10^(-3) mm thick (mu_(g)=1.5) is placed in the path of one of the interfering beams in a Yongs's double slit interference arrangement using monochromatic light of wavelenght 6000 A. If the central bright fringe shifts a distance equal to width of 10 bands. What is the thickness of the sheet of diamond of refractive index 2.5 that has to be introduced in the path of second beam to bring th ecentral bright fringe to original position?

The young's double slit experiment is done in a medium of refractive index 4//3 .A light of 600nm wavelength is falling on the slits having 0.45 mm separation .The lower slit S_(2) is covered by a thin glass sheet of thickness 10.4mu m and refractive index 1.5 .the intereference pattern is observed ona screen placed 1.5m from the slits are shown (a) Find the location of the central maximum (bright fringe with zero path difference)on the y-axis. (b) Find the light intensity at point O relative to the maximum fringe intensity. (c )Now,if 600nm light is replaced by white light of range 400 to700 nm find the wavelength of the light that from maxima exactly point O .[All wavelengths in this problem are for the given medium of refractive index 4//3 .Ignore dispersion]

Two identical glass rods S_(1) and S_(2) (refractive index=1.5) have one convex end of radius of curvature 10 cm. They are placed with the curved surfaces at a distance d as shown in the figure, with their axes (shown by the dashed line) aligned. When a point source of light P is placed inside rod S_(1) on its axis at a distance of 50 cm from the curved face, the light rays emenating from it are found to be parallel to the axis inside S_(2) . The distance d is

In Young's double slit experiment the slits, S_(1) & S_(2) are illuminated by a parallel beam of light of wavelength 4000 Å from the medium of refractive index n_(1)=1.2 A thin film of thickness 1.2 mum and refractive index n=1.5 is placed infrom of S_(1) perpedicular to path of light. the refractive index of medium between plane of slits & screen is n_(2)=1.4 if the light coming from the film and S_(1)&S_(2) have equal intensities I then intensity at geometrical centre of the screen O is

In a thin spherical fish bowl of radius 10 cm filled with water of refractive index (4//3) , there is a small fish at a distance 4 cm from the centre C as shown in Figure. Where will the fish appear to be, if seen from (a) E and (b) F (neglect the thickness of glass)?

A vessel ABCD of 10 cm width has two small slits S_(1) and S_(2) sealed with idebtical glass plates of equal thickness. The distance between the slits is 0.8 mm . POQ is the line perpendicular to the plane AB and passing through O, the middle point of S_(1) and S_(2) . A monochromatic light source is kept at S, 40 cm below P and 2 m from the vessel, to illuminate the slits as shown in the figure. Calculate the position of the central bright fringe on the other wall CD with respect of the line OQ . Now, a liquid is poured into the vessel and filled up to OQ . The central bright fringe is fiund to be at Q. Calculate the refractive index of the liquid.

A screen is at distance D = 80 cm form a diaphragm having two narrow slits S_(1) and S_(2) which are d = 2 mm apart. Slit S_(1) is covered by a transparent sheet of thickness t_(1) = 2.5 mu m slit S_(2) is covered by another sheet of thikness t_(2) = 1.25 mu m as shown if Fig. 2.52. Both sheets are made of same material having refractive index mu = 1.40 Water is filled in the space between diaphragm and screen. Amondichromatic light beam of wavelength lambda = 5000 Å is incident normally on the diaphragm. Assuming intensity of beam to be uniform, calculate ratio of intensity of C to maximum intensity of interference pattern obtained on the screen (mu_(w) = 4//3)

In the figure shown S is a point monochromatic light source of frequency 6xx10^(14)Hz .M is a concave mirror of radius of curvature 20 cm and L is a thin converging lens of focal length 3.75 cm AB is the principal axis of M and L. Light reflected from the mirror and refracted from the lens in succession reaches the screen. An interference pattern is obtained on the screen by this arrangement. Q. Distance between two coherent sources whichmakes interference pattern on the screen is

Two parallel beams of light P and Q (separation d) containing radiations of wavelengts 4000Å and 5000 Å (which are mutually coherent in each wavelength separately) are incident normally on a prism as shown in figure the refractive index of the prism as a function of wavelength is given by the relation mu(lamda)=1.20+(b)/(lamda^(2)) where lamda is in Å and b is a positive constant. The value of b is such that the condition for total reflection at the face AC is just satisfied for one wavelength and is not satisfied for the other. A convergent lens is used to bring these transmitted beams into focus. If the intensities of the upper and the lower beams immediately after transmission from the face AC, are 4I and I respectively, find the resultant intensity at the focus.

In the figure shown S is a point monochromatic light source of frequency 6xx10^(14)Hz .M is a concave mirror of radius of curvature 20 cm and L is a thin converging lens of focal length 3.75 cm AB is the principal axis of M and L. Light reflected from the mirror and refracted from the lens in succession reaches the screen. An interference pattern is obtained on the screen by this arrangement. Q. If the lens is replaced by another converging lens of focal length (10)/(3)cm and the lens is shifted towards right by 2.5 cm then

Home
Profile