Question

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

• A. $12.5\text{cm}$
• B. $25\text{cm}$
• C. $\frac{50}{3}\text{cm}$
• D. $18\text{cm}$

Answer 1

The correct option is B $25\text{cm}$

Since, there is no parallax between the images formed by two mirrors, it means that both images by plane mirror and convex mirror are coinciding each other.



Given, $\text{Distance between the plane mirror and object}=30\text{cm}\text{Distance between the convex mirror and object}=50\text{cm}$

According to a property of plane mirror, it will form an image at a distance of $30\text{cm}$ behind it.

Hence, for the convex mirror,

$u=-50\text{cm};v=+10\text{cm}$

Using the mirror formula,

$\frac{1}{f}=\frac{1}{v}+\frac{1}{u}$

$\Rightarrow \frac{1}{f}=\frac{1}{+10}+\frac{1}{-50}=\frac{4}{50}$

$\Rightarrow f=\frac{25}{2}\text{cm}$

$\Rightarrow R=2f=25\text{cm}$

<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Hence, $\left(B\right)$ is the correct answer.