Question

6. A man is using a concave mirror for shaving. If his
face is 20 cm from the mirror having magnification
2, what will be the radius of curvature of the mirror ?
[Ans. 80 cm]
16​

Answer 1

Explanation:

R = 20cm, f = R/2 =10cm

P = ? (Distance of the object)

q =2p (from definition of magnification)

Formula for concave mirror is

1/f = 1/p + 1/q

1/f = 1/p + 1/2p

1/f = 3/2p

P = 3f/2 =(3×10cm)/2

P = 15cm

Answer 2

Step by Step explanation:

Given: $R=20cm$, and magnification is $2$.

To find: The radius of curvature

For the calculation of the radius of curvature,

We know that  $R=20cm$,

∴ $F=\frac{R}{2}$

⇒ $F=\frac{20}{2}$

⇒ $10cm$

The formula for a concave mirror is $\frac{1}{F} = \frac{1}{P} + \frac{1}{Q}$

We know that $Q=2P$

Thus,

⇒ $\frac{1}{F} = \frac{1}{P} + \frac{1}{2P}$

⇒ $\frac{1}{F} = \frac{3}{2P}$

⇒$P=\frac{3F}{2}$

⇒$P=\frac{3x10}{2}$

⇒$\frac{30}{2}$

⇒$15cm$

The radius of curvature is $15cm$.