Optics 3 Question 42

42. A pin is placed 10cm in front of a convex lens of focal length 20cm and made of a material of refractive index 1.5. The convex surface of the lens farther away from the pin is silvered and has a radius of curvature of 22cm. Determine the position of the final image. Is the image real or virtual ?

(1978)

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Answer:

Correct Answer: 42. at a distance of 11 cm, virtual

Solution:

  1. The given system behaves like a mirror of power given by P=2PL+PM

or 1F=210.2+20.22

As PL=1f(m)

and PM=1f(m)=2R(m)

Solving this equation, we get

F=1.1m=110cm

i.e. the system behaves as a concave mirror of focal length 18.33cm.

Using the mirror formula

1v+1u=1f we have 1v110=1110orv=11cm

i.e. virtual image will be formed at a distance of 11cm.



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