Question 71: Ray Optics

Question

A point object is placed at a distance of 20 cm from a thin plano-convex lens of focal length 15 cm , if the plane surface is silvered. The image will form at

Accepted Answer

Focal length of the lens is given by
$$ f=\frac{\mathrm{R}}{\mu-1}=15 $$
After silvering the plane surface of the lens, it converts into the thin plano-convex mirror.
Focal length is now changed.
$	herefore$ For mirror, new focal length $f$ is given by
$$ f^{\prime}=\frac{R}{2(\mu-1)}=\frac{15}{2}=7.5 $$
Thus, for the mirror, equation becomes,
$$ \begin{gathered} \frac{1}{v}+\frac{1}{u}=\frac{1}{f^{\prime}} \ {[u=	ext { object distance from mirror }=-20 \mathrm{~cm}} \ v=	ext { image distance from mirror }=?] \ \frac{1}{v}+\frac{1}{-20}=\frac{1}{-7.5} \end{gathered} $$
$$ \begin{aligned} & \frac{1}{v}=-\frac{1}{7.5}+\frac{1}{20}=\frac{-20+7.5}{7.5 	imes 20} \ & \frac{1}{v}=\frac{-12.5}{150} \ & v=\frac{-150}{12.5} \ & v=-12 \mathrm{~cm} \end{aligned} $$
$	herefore-\operatorname{sign}$ Indicates that it is to the left of the system.

Answer

60 cm left of AB

Answer

30 cm left of $A B$

Answer

12 cm left of AB

Answer

60 cm right of AB

Ray Optics

A point object is placed at a distance of 20 cm from a thin plano-convex lens of focal length 15 cm , if the plane surface is silvered. The image will form at

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