Question

If AB = 10 cm & DB = 40 cm (diameter). What is the radius of curvature and the focal length of the spherical glass respectively?

• A. 40 cm, 5 cm
• B. 20 cm, 10 cm
• C. 20 cm, 20 cm
• D. 40 cm, 10 cm

Answer 1

The correct option is B 20 cm, 10 cm

Solution 1:
Focus is at point A since parallel rays after reflection pass through point A. Since AB is equal to 10 cm, the focal length is equal to 10 cm.
$f=-10cm$

Now, focal length is half the radius of curvature. So,
$f=\frac{R}{2}$
$R=2f=-20cm$

Solution 2:
Diameter of the sphere, $d=DB=40cm$
Radius of curvature is half of diameter.
$R=-d/2=-20cm$

Now, focal length (f) is half of the radius of curvature.
$f=\frac{R}{2}=-10cm$