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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CBSE Class 12 Sample Paper for 2022 Boards [Term 2] - Physics
CBSE Class 12 Sample Paper for 2022 Boards [Term 2] - Physics
Last updated at Dec. 14, 2024 by Teachoo
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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 đ_(đ_đ )=1.5 Focal length of the given convex lens when it is placed in air is đ=+20 đđ Refractive index of the given medium with respect to air is đ_(đ_đ )=1.25 New focal length of the given convex lens when placed in a medium is fâ 1/đ=(đ_(đ_đ )â1) [(1/đ _1 )+(1/đ ^2 )] Given đ_(đ_đ )=1.5 Focal length of the given convex lens when it is placed in air is đ=+20 đđ Refractive index of the given medium with respect to air is đ_(đ_đ )=1.25 New focal length of the given convex lens when placed in a medium is fâ 1/đ=(đ_(đ_đ )â1) [(1/đ _1 )+(1/đ ^2 )] 1/đ=(đ_(đ_đ )â1) [(1/đ _1 )+(1/đ ^2 )] Dividing (A) by (B), we get đâ˛/đ=((đ_(đ_đ ) â 1))/((đ_(đ_đ )â 1))=((1.5 â 1))/((1.2 â 1))=0.5/0.2=5/2=2.5 đ^â˛=2.5đ=(2.5 Ă20)đđ= +50 đđ as đ_(đ_đ )= đ_đ/đ_đ =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.