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The focal length of a convex lens made of glass of refractive index (1.5) is 20 cm. What will be its new focal length when placed in a medium of refractive index 1.25 ? Is focal length positive or negative? What does it signify? 

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Question 10 The focal length of a convex lens made of glass of refractive index (1.5) is 20 cm. What will be its new focal length when placed in a medium of refractive index 1.25 ? Is focal length positive or negative? What does it signify? Given 𝑎_(𝜇_𝑔 )=1.5 Focal length of the given convex lens when it is placed in air is 𝑓=+20 𝑐𝑚 Refractive index of the given medium with respect to air is 𝑎_(𝜇_𝑚 )=1.25 New focal length of the given convex lens when placed in a medium is f’ 1/𝑓=(𝑎_(𝜇_𝑔 )−1) [(1/𝑅_1 )+(1/𝑅^2 )] Given 𝑎_(𝜇_𝑔 )=1.5 Focal length of the given convex lens when it is placed in air is 𝑓=+20 𝑐𝑚 Refractive index of the given medium with respect to air is 𝑎_(𝜇_𝑚 )=1.25 New focal length of the given convex lens when placed in a medium is f’ 1/𝑓=(𝑎_(𝜇_𝑔 )−1) [(1/𝑅_1 )+(1/𝑅^2 )] 1/𝑓=(𝑚_(𝜇_𝑔 )−1) [(1/𝑅_1 )+(1/𝑅^2 )] Dividing (A) by (B), we get 𝑓′/𝑓=((𝑎_(𝜇_𝑔 ) − 1))/((𝑚_(𝜇_𝑔 )− 1))=((1.5 − 1))/((1.2 − 1))=0.5/0.2=5/2=2.5 𝑓^′=2.5𝑓=(2.5 ×20)𝑐𝑚= +50 𝑐𝑚 as 𝑚_(𝜇_𝑔 )= 𝜇_𝑔/𝜇_𝑚 =1.5/1.25=1.2 New focal length is positive. The significance of the positive sign of the focal length is that given Convex lenses still converging in the given medium.

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.