Question

In a spherical mirror, the distance between the focus point and centre of curvature is \( 20 \, \text{cm} \). Calculate the following and write their names: (i) The distance of pole of mirror from its focal point.
(ii) The distance of pole of mirror from its centre of curvature. \vspace{0.5cm} (i) The distance of pole of mirror from its focal point

Hint:

In spherical mirrors, the focal length is half of the radius of curvature, given by \( f = \frac{R}{2} \). The radius of curvature is always twice the focal length in spherical mirrors.

Answer 1

Step 1: The focal length \( f \) of a spherical mirror is the distance between the pole and the focal point. 

Step 2: Given that the distance between the focus and centre of curvature is \( 20 \, \text{cm} \), we know that: \[ f = 20 \, \text{cm} \] \[ \boxed{20 \, \text{cm} \text{ (Focal length)}} \] 

(ii) The distance of pole of mirror from its centre of curvature

Solution: 

Step 1: The radius of curvature \( R \) is the distance between the pole and the centre of curvature. 

Step 2: Since the focal length is given as \( f = 20 \, \text{cm} \), we use the relation: \[ R = 2f \] 

Step 3: Substituting the given value: \[ R = 2 \times 20 = 40 \, \text{cm} \] \[ \boxed{40 \, \text{cm} \text{ (Radius of curvature)}} \]