Question

Question details is given in picture below?

Answer 1

`mu=2-y/x`

Explanation:

It is easy to see that for the needle to coincide with the image, the object must be placed at the focus of the lens - so that after refraction through the lens, light emerges as a parallel beam, falls normally on the mirror and is reflected right back, converging back at the focus on its return journey. So, the distance between the lens and the object must be equal to the focal length of the lens in magnitude.

Thus, the effective focal length of the glass lens + liquid lens combination is `x`, while that of the glass lens alone is `y` . Hence the focal length of the lens formed by the plano-concave layer of liquid is `(1/y-1/x)^-1` .

Now, using the lens-maker's formula, we have

`1/y = (1.5-1)times 2/R = 1/R`

and again, for the liquid lens

`1/y-1/x=(mu-1)(1/R-1/oo)=(mu-1)/R = (mu-1)/y`

Thus

`mu-1 = 1-y/x implies mu=2-y/x`