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Q.

The power of a convex mirror with a radius of curvature of $50 cm$ is,

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a

+ 4 D

b

+ 3 D

c

- 0.25 D

d

+ 1.5 D

answer is A.

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Detailed Solution

The power of the convex mirror is

+ 4 D

.
The radius (R) of the curvature of the mirror is the distance between the centre of the curvature of the mirror and the pole of the mirror. The distance between the focus and pole is called focal length(F), and it is half of the radius(R) of the curvature of the mirror.
Given that,

Radius of curvature (R) = + 30 cm

[Positive: as the mirror is convex]
As we know that

F =

\frac{R}{2}

F = \frac{50}{2}

F = + 25 cm

Or,

F = 0.25 m

The focal length of the convex mirror is

0.25 m

.
We know the power of a mirror is the reciprocal of the focal length of the mirror in meters. Mathematically,

Power (P) = \frac{1}{F (in meters)}

So,

P = \frac{1}{0.25}

\Rightarrow P = + 4 D

Diopter(

D

) is the SI unit of the power.

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