Question

A convex lens of focal length 20 cm and another plano convex lens of focal length 40 cm are placed co-axially (see figure). The plano convex lens is silvered on plane surface. For what value ( or ) values of (in cm) so that final image of the object ‘O’ is formed on O itself.
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Answer 1

Thus the value of d in cm is d = 20 cm

Explanation:

Using lens mirror formula for plano convex lens:

1 / f = 1 / 40 = (μ − 1 ) R  --------(i)

For lens:

1 / v 1 − 1 / 10 = 1 / 20

v1 = - 20 cm

Distance of f1 from plano convex lens is "d + 20 cm".

v2 / v - u1 / u = u2 - u1 / R

u / ∞  - 1 / - ( d + 20) = u - 1 / R

=> 1/ d + 20 = u - 1 / R

From equation (1) we get.

1 / d + 20 = 1 / 40

d + 20 = 40

d = 40 - 20 = 20 cm

Thus the value of d in cm is 20 cm