Question

An object is placed in front of a convex mirror at a distance of 50cm. A plane mirror is introduced covering the lower half of the convex mirror. If the distance between the object and the plane mirror is 30cm, it is found that there is no parallax between the images formed by the two mirrors. The radius curvature of the convex mirror is :

• A. 12.5 cm
• B. 20 cm
• C. 25 cm
• D. 30 cm

Answer 1

Answer: (C)

25 cm

Distance at which the image due to mirror plane is $10cm$ from pole of convex mirror,

From mirror formula, $\frac{1}{10}-\frac{1}{50}=\frac{1}{f}$

$\frac{1}{f}=\frac{\text{/}{4}^2}{\text{/}{50}_{25}}$

Focal length, $f=\frac{25}{2}$

Radius of curvature, $R=2f=25cm$