Question 41: Ray Optics

Question

A mirror is used to produce an image with magnification of $\frac{1}{4}$. If the distance between object and its image is 40 cm, then the focal length of the mirror is ________.

Accepted Answer

Magnification for a mirror is
$$m=-\frac{v}{u}$$
Given $m=\frac{1}{4}$, so
$$-\frac{v}{u}=\frac{1}{4}\;\Rightarrow\; v=-\frac{u}{4}$$
For a real object, $u0$.
Let $u=-x$ (where $x>0$). Then
$$v=-\frac{-x}{4}=\frac{x}{4}$$
Distance between object and image (object in front, image behind) is
$$x+v=40$$
$$x+\frac{x}{4}=40$$
$$\frac{5x}{4}=40 \Rightarrow x=32\ 	ext{cm}$$
So,
$$u=-32\ 	ext{cm},\quad v=+8\ 	ext{cm}$$
Now use mirror formula:
$$\frac{1}{f}=\frac{1}{v}+\frac{1}{u}=\frac{1}{8}-\frac{1}{32}=\frac{4-1}{32}=\frac{3}{32}$$
$$f=\frac{32}{3}\approx 10.7\ 	ext{cm}$$
Correct option: C) $10.7\ 	ext{cm}$

Answer

10 cm

Answer

12.7 cm

Answer

10.7 cm

Answer

15 cm

Ray Optics

A mirror is used to produce an image with magnification of \frac{1}{4}. If the distance between object and its image is 40 cm, then the focal length of the mirror is ________.

Choose the correct answer: