Question

A point object form a real, enlarged image, in front of concave mirror of curative radius 40 cm if the distance between the object and the image be 30 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 B 30 cm

Radius of curvature (r) = 40 cm

$\text{v - u = 30 cm}$

Focal length of the mirror is given by the formula

$\text{f =}\frac{\text{r}}{\text{2}}$

$\Rightarrow \text{f =}\frac{40}{2}=20\text{cm}$

According to the sign conventions, the mirror formula for a concave mirror is

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

Substituting the values,

$\frac{\text{1}}{\text{- 20}}\text{=}\frac{\text{1}}{\text{- (u + 30)}}\text{+}\frac{\text{1}}{\text{- u}}$

$\frac{\text{1}}{\text{20}}\text{=}\frac{\text{u + (u + 30)}}{\text{u(u + 30)}}$

${\text{u}}^2+\text{30u = 40u + 600}$

${\text{u}}^2\text{- 10u - 600 = 0}$

$\text{u = 30 or u = - 20}$

As already sign conventions are applied, the value of u should be positive

Therefore, the object distance will be 30 cm.