Question

Q: An object is placed at a distance of 25cm from the pole of a convex mirror and a plane mirror is set so that the virtual images formed by the two mirrors don't have any parallax. The plane mirror is 20 cm from the object. The focal length of mirror is
A. 37.5cm
B. 30 cm
C. 75 cm
D. 60 cm

Answer 1

We can write the mirror equation for a convex mirror as

$$\frac{1}{f} = \frac{1}{d_o} - \frac{1}{d_i} (1)$$

where f is the focal length, d₀ is the object distance, di the image distance

Using (1) we got:

$$f=\frac{( d_i \times d_i)}{d_i- d_o} (2)$$

where d₀ = 25 cm

A convex mirror and plane mirror form two virtual images of the object. The two virtual image so formed coincide because the virtual images formed by the two mirrors don't have any parallax.

The image distance is equal to: d_i=20 cm+20 cm – 25 cm = 15 cm

We find using (2): f = - 37.5 m

Answer:

A. 37.5cm