Question

An air bubble is situated at a distance of 1.2 cm from the surface of a solid sphere of glass having diameter 4.0 . find the position of the image of the bubble along the diameter of the sphere .refractive index of the glass is 1.5

Answer 1

Hi there.

Refractive Index of the glass(μ₁) = 1.5

Refractive Index of the air(μ₂) = 1

Diameter of the Convex Surface(d) = 10 cm.

∴ Radius of the Convex surface(r) =  5 cm. (negative)

Real Depth of the Air Bubble (u) = 3 cm. (negative)

Let the Apparent Depth of the Air bubble (or the distance of the image of the bubble from the air surface) = v cm.

∵ When the light from the bubble goes from the glass to the air, then  

μ₂/v - μ₁/u = (μ₂ - μ₁)/r

∴ 1/v - 1.5/-3 = (1.5 - 1)/-5

⇒ 1/v + 1/2 = 0.5/-5

⇒ 1/v = -1/2 - 1/10

⇒ 1/v = (-5 - 1)/10

⇒ 1/v = -6/10

∴ v = -10/6 cm.

∴ v = -5/3

∴ v = -1.67 cm 

Hence, the image is formed at the distance of 1.67 cm from the convex surface.

Hope it helps.