A spherical interface of radius R separates two media of refractive indices:

• n₁ = 1
• n₂ = 1.4

A point object is placed at a distance 4R from the spherical surface.

Find the magnitude of magnification produced by the refracting surface.

Options:

• (1) 1.66
• (2) 1.33
• (3) 2.33
• (4) 2.66

For refraction at a spherical surface:

n₂/v − n₁/u = (n₂ − n₁)/R

Given:

• n₁ = 1
• n₂ = 1.4
• u = −4R
• R = +R

Substituting:

1.4/v − 1/(−4R) = 0.4/R

1.4/v + 1/(4R) = 0.4/R

1.4/v = 0.4/R − 0.25/R

= 0.15/R

v = 1.4R / 0.15

= 28R/3

Magnification:

m = (n₁v)/(n₂u)

= (1 × 28R/3) / (1.4 × 4R)

= 28/16.8

= 1.67

Therefore:

|m| ≈ 1.66

Final Answer

Option (1) 1.66