Ray Optics and Optical Instruments - Result Question 41

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42. The radius of curvature of a thin plano-convex lens is $10 cm$ (of curved surface) and the refractive index is 1.5. If the plane surface is silvered, then it behaves like a concave mirror of focal length

======= ####42. The radius of curvature of a thin plano-convex lens is $10 cm$ (of curved surface) and the refractive index is 1.5. If the plane surface is silvered, then it behaves like a concave mirror of focal length

3e0f7ab6f6a50373c3f2dbda6ca2533482a77bed:content/english/neet-pyq-chapterwise/physics/ray-optics-and-optical-instruments/ray-optics-and-optical-instruments—result-question-41.md (a) $10 cm$

(b) $15 cm$

(c) $20 cm$

(d) $5 cm$

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Answer:

Correct Answer: 42. (a)

Solution:

  1. (a) The silvered plano convex lens behaves as a concave mirro; whose focal length is given by $\frac{1}{F}=\frac{2}{f_1}+\frac{1}{f_m}$

If plane surface is silvered

$f_m=\frac{R_2}{2}=\frac{\infty}{2}=\infty$

$\therefore \frac{1}{f_1}=(\mu-1)(\frac{1}{R_1}-\frac{1}{R_2})$

$=(\mu-1)(\frac{1}{R}-\frac{1}{\infty})=\frac{\mu-1}{R}$

$\therefore \frac{1}{F}=\frac{2(\mu-1)}{R}+\frac{1}{\infty}=\frac{2(\mu-1)}{R}$

$F=\frac{R}{2(\mu-1)}$

Here, $R=10 cm, \mu=1.5$

$\therefore F=\frac{10}{2(1.5-1)}=10 cm$

43 .

(b) $R_1=60 cm, R_2=\infty, \mu=1.6$

$\frac{1}{f}=(\mu-1)(\frac{1}{R_1}-\frac{1}{R_2})$

$\frac{1}{f}=(1.6-1)(\frac{1}{60}) \Rightarrow f=100 cm$.