Question

A point object forms a real, enlarged image, in front of a concave mirror of radius of curvature 10 cm. If the distance between the object and the image be 20 cm, then the object distance will be:

• A. 10 cm
• B. 30 cm
• C. 40 cm
• D. 60 cm

Answer 1

The correct option is A 10 cm

Given, radius of curvature $R=10m$
Focal length,f = $\frac{R}{2}$ = $\frac{10}{2}=5cm$.
Distance between the image and the object = 20 cm
Let distance of mirror from the object and the image be $u$ and $v$ respectively.
Since an enlarged real image is being formed in a concave mirror, so the object must be between focus and centre of curvature and the image must be formed beyond centre of curvature.
So, taking $u$ and $v$ with proper sign we have $u-v=20cm$
Take $v=u-20$, $f=-5cm$ and object distance $=-u$. (because it's a concave mirror)

Using mirror formula, $\frac{1}{\text{f}}=$ $\frac{1}{\text{v}}+$ $\frac{1}{\text{u}}$ with the sign convention for the concave mirror
We get, $\frac{1}{-5}=$ $\frac{1}{-(u+20)}+$ $\frac{1}{\text{-u}}$
$=u^2+20u+100=0$
solving the equation we will get,
$-u=10cm$
Negative sign shows that object is kept on the left side of the mirror.