Assertion `:` A double convex lens `(mu=1.5)` has focal length `10 cm`. When the lens is immersed in water `(mu=4//3)` its focal length becomes `40 cm`.
Reason `:` `(1)/(f)=(mu_(1)-mu_(m))/(mu_(m))((1)/(R_(1))-(1)/(R_(2)))`

Options

A. If both assertion and reason are ture and reason is the correct explanation of assertion
B. If both assertion and reason are true but reason is not the correct explanation of assertion
C. If assertion is true but reason is false
D. If both assertion and reson are false.

Answer

A

Explanation

`1/f = (""^(a) mu_(g) - 1) [(1)/(R_(1)) - (1)/(R_(2))] = ((mu_(g))/(mu_(w)) - 1) ((1)/(R_(1)) - (1)/(R_(2)))`
`(1)/(f) = ((mu_(g) - mu_(w))/(mu_(w))) * [(1)/(R_(1)) - (1)/(R_(2))] = ((1.5 - 1.33)/(1.33)) * [(1)/(20) + (1)/(20)]`
` (1)/(f) = (0.13 xx 2)/(20) implies f = (20)/(0.26)`
`therefore f = 76.92` cm .