Question

A point source, in air, is placed at a distance of 6 cm in front of a convex spherical surface (n = 1.5 and radius of curvature = 24 cm). Find the position and nature of the image formed.

Answer 1

Given: Refractive index of first medium, air (n₁) = 1.0

Refractive index of second medium, glass (n₂) = 1.5

Object distance (u) = −6 cm

Radius of curvature (R) = +24 cm (positive for convex surface)

To find the position and nature of the image formed by a convex spherical surface, we use the refraction formula for a single spherical surface:

`n_2/v - n_1/u = (n_2 - n_1)/R`

⇒ `1.5/v - 1/-6 = (1.5 - 1)/24`

⇒ `1.5/v + 1/6 = 0.5/24`

⇒ `1.5/v = 0.5/24 - 1/6`

Converting R.H.S. to a common denominator 24:

⇒ `1.5/v = 0.5/24 - 4/24`

⇒ `1.5/v = -3.5/24`

v = `(1.5 xx 24)/-3.5`

= `36/3.5`

≈ −10.29 cm

∴ The image is formed at a distance of approximately 10.29 cm from the pole on the same side as the object. Since v is negative, the image is virtual.