Question

a glass sphere ( n= 1.5 ) 4 CM in diameter has a Luminous speck O embedded inside the sphere 1 cm below the surface find where it will appear to be when vied along adiametre of the sphere from the near surface
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Answer 1

The distance of the image is 1.125 cm.

Explanation:

The  refraction of light from the spherical surface is given by the formula:

n₂/v - n₁/u + = [n₂ – n₁][1/R]

Where,

n₁ = Refractive index of air = 1 (known)

n₂ = Refractive index of glass = 1.5 (given)

u = Distance of the object = 4 cm - 1 cm = 3 cm

v = Distance of the image

R = Radius of the curvature = 4/2 = 2 cm

On substituting the values, we get,

1.5/v - 1/3 = (1.5 - 1)/2

1.5/v - 1/3 = 0.5 × 2

1.5/v - 1/3 = 1

1.5/v = 1 + 1/3

1.5/v = (3 + 1)/3

1.5/v = 4/3

v = 1.5 × 3/4 = 4.5/4

∴ v = Image distance = 1.125 cm