STATEMENT-1 The focal length of a lens d...

STATEMENT-`1` The focal length of a lens does not depend on the medium in which it is submerged.
`STATEMENT-`2 `(1)/(f)=(mu_(2)-mu_(1))/(mu_(1))((1)/(R_(1))-(1)/(R_(2)))`

Statement is True, Statement II is True, Statement II is correct explanation for Statement I

Statement I is True, Statement II is True, Statement II is NOT a correct explanation for Statement I.

Statement I is True, Statement II is False.

Statement I is False, Statement II is True.

Text Solution

AI Generated Solution

The correct Answer is:

To solve the question, we need to analyze both statements provided and determine their validity based on the principles of geometrical optics. ### Step-by-Step Solution: **Step 1: Analyze Statement 1** - Statement 1 claims that "The focal length of a lens does not depend on the medium in which it is submerged." - In optics, the focal length of a lens is influenced by the refractive indices of the lens material and the surrounding medium. When a lens is submerged in a different medium, the effective refractive index changes, which in turn affects the focal length. **Conclusion for Step 1:** - Therefore, Statement 1 is **false** because the focal length does depend on the medium. **Step 2: Analyze Statement 2** - Statement 2 provides the formula: \(\frac{1}{f} = \frac{\mu_2 - \mu_1}{\mu_1}\left(\frac{1}{R_1} - \frac{1}{R_2}\right)\). - This formula relates the focal length \(f\) of a lens to the refractive indices (\(\mu_1\) for the medium in which the lens is placed and \(\mu_2\) for the lens material) and the radii of curvature (\(R_1\) and \(R_2\)) of the lens surfaces. **Conclusion for Step 2:** - The formula is indeed correct and shows that the focal length is dependent on the refractive indices. Thus, Statement 2 is **true**. **Final Conclusion:** - Statement 1 is false, and Statement 2 is true. ### Summary: - **Statement 1**: False - **Statement 2**: True

Topper's Solved these Questions

GEOMETRICAL OPTICS
CENGAGE PHYSICS ENGLISH|Exercise Assertion-Reasoninig|2 Videos
GEOMETRICAL OPTICS
CENGAGE PHYSICS ENGLISH|Exercise Linked Comprehension|51 Videos
GEOMETRICAL OPTICS
CENGAGE PHYSICS ENGLISH|Exercise Subjective|26 Videos
ELECTRON,PHONTS,PHOTOELECTRIC EFFECT & X-RAYS
CENGAGE PHYSICS ENGLISH|Exercise dpp 3.3|15 Videos
HEATING EFFECT OF CURRENT
CENGAGE PHYSICS ENGLISH|Exercise Thermal Power in Resistance Connected in Circuit|27 Videos

Similar Questions

Explore conceptually related problems

The focal length of equiconvex lens of retractive index, mu=1.5 and radius of curvature, R is

Statement-1 : A glass convex lens (refractive index, mu_(1)=1.5 ), when immersed in a liquid of refractive index mu_(2)=2 , functions as a diverging lens. Statement-2 : The focal length of a lens is given by (1)/(f)=(mu-1)((1)/(R_(1))-(1)/(R_(2))) , where mu is the relative refractive index of the material of the lens with respect to the surrounding medium.

A thin lens of focal length + 12 cm is immersed in water (mu = 1.33). What is its new focal length ?

A uniform rope of length l lies on a table . If the coefficient of friction is mu , then the maximum length l_(1) of the part of this rope which can overhang from the edge of the table without sliding down is : (1)/(mu) (l)/(mu+1) (mul)/(1+mu) (mul)/(1-mu)

The image of a white object in with light formed by a lens is usually colored and blurred. This defect of image is called chromatic aberration and arises due to the fact that focal length of a lens is different for different colours. As R . I . mu of lens is maximum for violet while minimum for red, violet is focused nearest to the lens while red farthest from it as shown in figure. As a result of this, in case of convergent lens if a screen is placed at F_(v) center of the image will be violet and focused while sides are red and blurred. While at F_(R) , reverse is the case, i.e ., center will be red and focused while sides violet and blurred. The differece between f_(v) and f_(R) is a measure of the longitudinal chromatic aberration (L.C.A),i.e., L.C.A.=f_(R)-f_(v)=-df with df=f_(v)-f_(R) ........... (1) However, as for a single lens, (1)/(f)=(mu-1)[(1)/(R_(1))-(1)/(R_(2))] ............. (2) rArr -(df)/(f^(2))=dmu[(1)/(R_(1))-(1)/(R_(2))] ............... (3) Dividing E1n. (3) by (2) : -(df)/(f)=(dmu)/((mu-1))=omega, [omega=(dmu)/((mu-1))] "dispersive power" , .........(4) And hence, from Eqns. (1) and (4) , L.C.A.=-df=omegaf Now, as for a single lens neither f nor omega zero, we cannot have a single lens free from chromatic aberration. Condition of Achromatism : In case of two thin lenses in contact (1)/(F)=(1)/(F_(1))+(1)/(F_(2)) i.c,. -(dF)/(F^(2))=(df_(1))/(f_(1)^(2))-(df_(2))/(f_(2)^(2)) The combination will be free from chromatic aberration if dF=0 i.e., (df_(1))/(f_(1)^(2))+(df_(2))/(f_(2)^(2))=0 which with the help of Eqn. (4) reduces to (omega_(1)f_(1))/(f_(1)^(2))+(omega_(2)f_(2))/(f_(2)^(2))=0 , i.e., (omega_(1))/(f_(1))+(omega_(2))/(f_(2))=0 ........(5) This condition is called condition of achromatism (for two thin lenses in contact ) and the lens combination which satisfies this condition is called achromatic lems, from this condition, i.e., form Eqn. (5) it is clear the in case of achromatic doublet : Since, if omega_(1)=omega_(2), (1)/(f_(1))+(1)/(f_(2))=0 i.e., (1)/(F)=0 or F=infty i.e., combination will not behave as a lens, but as a plane glass plate. (2) As omega_(1) and omega_(2) are positive quantities, for equation (5) to hold, f_(1) and f_(2) must be of opposite nature, i.e., if one of the lenses is converging the other must be diverging. (3) If the achromatic combination is convergent, f_(C)ltf_(D) and as (f_(C))/(f_(d))=(omega_(C))/(omega_(D)), omega_(C)ltomega_(d) i.e., in a convergent achromatic doublet, convex lens has lesses focal legth and dispersive power than the divergent one. A combination is made of two lenses of focal lengths f and f' in contact , the dispersive powers of the materials of the lenses are omega and omega' . The combination is achromatic when :

The image of a white object in with light formed by a lens is usually colored and blurred. This defect of image is called chromatic aberration and arises due to the fact that focal length of a lens is different for different colours. As R . I . mu of lens is maximum for violet while minimum for red, violet is focused nearest to the lens while red farthest from it as shown in figure. As a result of this, in case of convergent lens if a screen is placed at F_(v) center of the image will be violet and focused while sides are red and blurred. While at F_(R) , reverse is the case, i.e ., center will be red and focused while sides violet and blurred. The differece between f_(v) and f_(R) is a measure of the longitudinal chromatic aberration (L.C.A),i.e., L.C.A.=f_(R)-f_(v)=-df with df=f_(v)-f_(R) ........... (1) However, as for a single lens, (1)/(f)=(mu-1)[(1)/(R_(1))-(1)/(R_(2))] ............. (2) rArr -(df)/(f^(2))=dmu[(1)/(R_(1))-(1)/(R_(2))] ............... (3) Dividing E1n. (3) by (2) : -(df)/(f)=(dmu)/((mu-1))=omega, [omega=(dmu)/((mu-1))] "dispersive power" , .........(4) And hence, from Eqns. (1) and (4) , L.C.A.=-df=omegaf Now, as for a single lens neither f nor omega zero, we cannot have a single lens free from chromatic aberration. Condition of Achromatism : In case of two thin lenses in contact (1)/(F)=(1)/(F_(1))+(1)/(F_(2)) i.c,. -(dF)/(F^(2))=(df_(1))/(f_(1)^(2))-(df_(2))/(f_(2)^(2)) The combination will be free from chromatic aberration if dF=0 i.e., (df_(1))/(f_(1)^(2))+(df_(2))/(f_(2)^(2))=0 which with the help of Eqn. (4) reduces to (omega_(1)f_(1))/(f_(1)^(2))+(omega_(2)f_(2))/(f_(2)^(2))=0 , i.e., (omega_(1))/(f_(1))+(omega_(2))/(f_(2))=0 ........(5) This condition is called condition of achromatism (for two thin lenses in contact ) and the lens combination which satisfies this condition is called achromatic lems, from this condition, i.e., form Eqn. (5) it is clear the in case of achromatic doublet : Since, if omega_(1)=omega_(2), (1)/(f_(1))+(1)/(f_(2))=0 i.e., (1)/(F)=0 or F=infty i.e., combination will not behave as a lens, but as a plane glass plate. (2) As omega_(1) and omega_(2) are positive quantities, for equation (5) to hold, f_(1) and f_(2) must be of opposite nature, i.e., if one of the lenses is converging the other must be diverging. (3) If the achromatic combination is convergent, f_(C)ltf_(D) and as (f_(C))/(f_(d))=(omega_(C))/(omega_(D)), omega_(C)ltomega_(d) i.e., in a convergent achromatic doublet, convex lens has lesses focal legth and dispersive power than the divergent one. Chromatic aberration of a lens can be corrected by :

The image of a white object in with light formed by a lens is usually colored and blurred. This defect of image is called chromatic aberration and arises due to the fact that focal length of a lens is different for different colours. As R . I . mu of lens is maximum for violet while minimum for red, violet is focused nearest to the lens while red farthest from it as shown in figure. As a result of this, in case of convergent lens if a screen is placed at F_(v) center of the image will be violet and focused while sides are red and blurred. While at F_(R) , reverse is the case, i.e ., center will be red and focused while sides violet and blurred. The differece between f_(v) and f_(R) is a measure of the longitudinal chromatic aberration (L.C.A),i.e., L.C.A.=f_(R)-f_(v)=-df with df=f_(v)-f_(R) ........... (1) However, as for a single lens, (1)/(f)=(mu-1)[(1)/(R_(1))-(1)/(R_(2))] ............. (2) rArr -(df)/(f^(2))=dmu[(1)/(R_(1))-(1)/(R_(2))] ............... (3) Dividing E1n. (3) by (2) : -(df)/(f)=(dmu)/((mu-1))=omega, [omega=(dmu)/((mu-1))] "dispersive power" , .........(4) And hence, from Eqns. (1) and (4) , L.C.A.=-df=omegaf Now, as for a single lens neither f nor omega zero, we cannot have a single lens free from chromatic aberration. Condition of Achromatism : In case of two thin lenses in contact (1)/(F)=(1)/(F_(1))+(1)/(F_(2)) i.c,. -(dF)/(F^(2))=(df_(1))/(f_(1)^(2))-(df_(2))/(f_(2)^(2)) The combination will be free from chromatic aberration if dF=0 i.e., (df_(1))/(f_(1)^(2))+(df_(2))/(f_(2)^(2))=0 which with the help of Eqn. (4) reduces to (omega_(1)f_(1))/(f_(1)^(2))+(omega_(2)f_(2))/(f_(2)^(2))=0 , i.e., (omega_(1))/(f_(1))+(omega_(2))/(f_(2))=0 ........(5) This condition is called condition of achromatism (for two thin lenses in contact ) and the lens combination which satisfies this condition is called achromatic lems, from this condition, i.e., form Eqn. (5) it is clear the in case of achromatic doublet : Since, if omega_(1)=omega_(2), (1)/(f_(1))+(1)/(f_(2))=0 i.e., (1)/(F)=0 or F=infty i.e., combination will not behave as a lens, but as a plane glass plate. (2) As omega_(1) and omega_(2) are positive quantities, for equation (5) to hold, f_(1) and f_(2) must be of opposite nature, i.e., if one of the lenses is converging the other must be diverging. (3) If the achromatic combination is convergent, f_(C)ltf_(D) and as (f_(C))/(f_(d))=(omega_(C))/(omega_(D)), omega_(C)ltomega_(d) i.e., in a convergent achromatic doublet, convex lens has lesses focal legth and dispersive power than the divergent one. The dispersive power of crown and fint glasses are 0.02 and 0.04 respectively. An achromtic converging lens of focal length 40 cm is made by keeping two lenses, one of crown glass and the other of flint glass, in contact with each other. The focal lengths of the two lenses are :

The image of a white object in with light formed by a lens is usually colored and blurred. This defect of image is called chromatic aberration and arises due to the fact that focal length of a lens is different for different colours. As R . I . mu of lens is maximum for violet while minimum for red, violet is focused nearest to the lens while red farthest from it as shown in figure. As a result of this, in case of convergent lens if a screen is placed at F_(v) center of the image will be violet and focused while sides are red and blurred. While at F_(R) , reverse is the case, i.e ., center will be red and focused while sides violet and blurred. The differece between f_(v) and f_(R) is a measure of the longitudinal chromatic aberration (L.C.A),i.e., L.C.A.=f_(R)-f_(v)=-df with df=f_(v)-f_(R) ........... (1) However, as for a single lens, (1)/(f)=(mu-1)[(1)/(R_(1))-(1)/(R_(2))] ............. (2) rArr -(df)/(f^(2))=dmu[(1)/(R_(1))-(1)/(R_(2))] ............... (3) Dividing E1n. (3) by (2) : -(df)/(f)=(dmu)/((mu-1))=omega, [omega=(dmu)/((mu-1))] "dispersive power" , .........(4) And hence, from Eqns. (1) and (4) , L.C.A.=-df=omegaf Now, as for a single lens neither f nor omega zero, we cannot have a single lens free from chromatic aberration. Condition of Achromatism : In case of two thin lenses in contact (1)/(F)=(1)/(F_(1))+(1)/(F_(2)) i.c,. -(dF)/(F^(2))=(df_(1))/(f_(1)^(2))-(df_(2))/(f_(2)^(2)) The combination will be free from chromatic aberration if dF=0 i.e., (df_(1))/(f_(1)^(2))+(df_(2))/(f_(2)^(2))=0 which with the help of Eqn. (4) reduces to (omega_(1)f_(1))/(f_(1)^(2))+(omega_(2)f_(2))/(f_(2)^(2))=0 , i.e., (omega_(1))/(f_(1))+(omega_(2))/(f_(2))=0 ........(5) This condition is called condition of achromatism (for two thin lenses in contact ) and the lens combination which satisfies this condition is called achromatic lems, from this condition, i.e., form Eqn. (5) it is clear the in case of achromatic doublet : Since, if omega_(1)=omega_(2), (1)/(f_(1))+(1)/(f_(2))=0 i.e., (1)/(F)=0 or F=infty i.e., combination will not behave as a lens, but as a plane glass plate. (2) As omega_(1) and omega_(2) are positive quantities, for equation (5) to hold, f_(1) and f_(2) must be of opposite nature, i.e., if one of the lenses is converging the other must be diverging. (3) If the achromatic combination is convergent, f_(C)ltf_(D) and as (f_(C))/(f_(d))=(omega_(C))/(omega_(D)), omega_(C)ltomega_(d) i.e., in a convergent achromatic doublet, convex lens has lesses focal legth and dispersive power than the divergent one. Chromatic aberration in the formation of image by a lens arises because :

Calculate the focal length of concave len in water (mu_(w)= 4/3) if the surface have radii equal to 60cm and 20cm. mu_(g)=1.5

STATEMENT - 1 : When a lens is placed in a medium for which mu is less than of the lens, its focal length is moer than focal length in air. STATEMENT - 2 : When the lens is placed in a medium for which mu is greater than that of the lens. The nature of the lens remains unchanged. STATEMENT - 3 : When a lens of focal length f is placed in a medium for which mu is same as that of the lens then the power of the lens becomes zero

CENGAGE PHYSICS ENGLISH-GEOMETRICAL OPTICS-Single Correct

A concave mirror forms an image of the sun at a distance of 12 cm from...
Text Solution
|
A real object is placed infront of a convex mirror (focal length f). I...
Text Solution
|
An object is moving towards a convex mirror with a constant velocity. ...
Text Solution
|
A person is looking at the flat surface of a transparent hemisphere of...
Text Solution
|
Refractive index of an equilateral prism is sqrt(2)
Text Solution
|
A convex lens made of glass (mu(0) = 3//2) hs focal length f in air. T...
Text Solution
|
In the situation as shown in Figure, (cos53^(@)=(3)/(5))
Text Solution
|
A plano-convex lens (f = 20 cm) is silvered at plane surface. The foca...
Text Solution
|
For a concave mirror
Text Solution
|
A linear object of size 1.5 cm is placed at 10 cm from a lens of focal...
Text Solution
|
Assertion:Although the surfaces of goggle lens are curved, It does not...
Text Solution
|
Statement I: A beam of white light enters the curved surface of a semi...
Text Solution
|
Statement I: A ray is incident from outside on a glass sphere surround...
Text Solution
|
Statement I: Keeping a point object fixed, if a plane mirror is moved,...
Text Solution
|
Statement I: Lights of different colors travel with different speeds i...
Text Solution
|
Statement I: A beam of light rays has been reflected from a rough sur...
Text Solution
|
STATEMENT-1 A virtual image can be photographed. STATEMENT- 2 Only a...
Text Solution
|
STATEMENT-1 The focal length of a lens does not depend on the medium i...
Text Solution
|
STATEMENT-1 We cannot produce a real image by plane or convex mirror u...
Text Solution
|
Statement I: A light ray is incident on a glass slab. Some portion of ...
Text Solution
|

STATEMENT-`1` The focal length of a lens does not depend on the medium in which it is submerged. `STATEMENT-`2 `(1)/(f)=(mu_(2)-mu_(1))/(mu_(1))((1)/(R_(1))-(1)/(R_(2)))`

Text Solution

Topper's Solved these Questions

Similar Questions

CENGAGE PHYSICS ENGLISH-GEOMETRICAL OPTICS-Single Correct

STATEMENT-`1` The focal length of a lens does not depend on the medium in which it is submerged.
`STATEMENT-`2 `(1)/(f)=(mu_(2)-mu_(1))/(mu_(1))((1)/(R_(1))-(1)/(R_(2)))`