First slide

Ray optics

Question

A lens forms a diminished and erect image of an object. The magnification is 1 / 4. Then the ratio of object distance to focal length is

Moderate

A

4 : 1
B

4 : 3
C

2 : 3
D

3 : 1

Solution

(4)
Since the image is diminished and erect, the lens must be a concave lens.
$\begin{array}{l} N o w \frac{v}{u} = \frac{1}{4} \Rightarrow v = \frac{u}{4} \\ ∴ G e n e r a l l e n s f o r m u l a i s \frac{1}{v} - \frac{1}{u} = \frac{1}{f} \\ ∴ \frac{1}{(- u / 4)} - \frac{1}{(- u)} - \frac{1}{(- f)} \\ \Rightarrow - \frac{3}{u} = - \frac{1}{f} \Rightarrow \frac{u}{f} = 3 \end{array}$

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