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A Plane convex lens of refractive index ...

A Plane convex lens of refractive index `mu_1` and focal length `f_1` is kept in contact with another plane concave lens of refractive index `mu_2` and focal length `f_2` If the radius of curvature of their spherical faces is R each and `f_1 = 3 f_2` then `mu_1 " and " mu_2` are related as:

A

`mu_1 + mu_2 = 3`

B

`3mu_1 - 2mu_1 = 1`

C

`3mu_2 - mu_1 = 1`

D

`3mu_1 - mu_2 = 2`

Text Solution

Verified by Experts

The correct Answer is:
D

`(1)/(f_1) = (mu_1 - 1) (1/R - 1/oo)`
`rArr f_1 = (R )/(mu_1 -1 )`
`(1)/(f_2) = (mu_2 - 1) (1/oo - 1/R) = (1- mu_2)/(R )`
` rArr f_2 = (R )/(1 - mu_2)`
` | f_1 | = 3 | f_2 | rArr (R )/(mu_1 - 1) = (3R)/(mu_2 - 1)`
` rArr mu_2 - 1 = 3 mu_1 - 3 rArr 3mu_1 - mu_2 = 2`
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