Question

The focal length of a plano concave lens is -10 cm then its focal length when its plane surface is polished is (n= 3/2)​

Answer 1

Answer:

Explanation:

Dispersive power of a lens ∝ 1μ-1 Thus ω1ω2 = μ2-1μ1-1 = 2 Thus μ2 = 2μ1 ... powers in the ratio 2 : 1, behave as an achromatic lens of focal length 10 cm. ... They will have zero longitudinal chromatic aberration if their dispersive powers are in ... focal length ′f ′ from achromatic combination when separated by distance ...

1 answer

Answer 2

Given :

Focal length of the given plano concave lens = -10 cm

Refractive index  ( n) = $\frac{3}{2}$

To Find :

What is its focal length when its plane surface is polished = ?

Solution :

When the plane surface is polished , then it becomes a combination of a concave lens and a plane mirror .

So now if a parallel beam of light comes , it will converge at a distance of 10 cm  in front of lens .

So this image will act as an object for the plane mirror and its image will be formed at a distance of 10 cm behind the plane mirror .

Now this image will act as an object for lens , and as :

$\frac{1}{v} - \frac{1}{u} = \frac{1}{f}$

So, $\frac{1}{v} + \frac{1}{f} = \frac{1}{f}$   ( ∴ image is formed at a distance 'f' opposite to

                              the side of focus )                              

Or , $v = \infty$

∴ Focus will shift to ∞

So u = -f

Hence , its focal length will be -(-10) cm = 10 cm .