Light from a point source in air falls on a convex curved surface of radius 20 cm and refractive index 1.5. If the source is located at 100 cm from the convex surface, the image will be formed at ________ cm from the object.

Solution

Physics sir · 4 steps

Get the image distance from the surface first, then add the object distance across it.

1. Set up signs. Light goes from air (μ₁ = 1) into glass (μ₂ = 1.5). Measure from the surface along the light: u = -100 cm. The centre of curvature is on the glass side, so R = +20 cm.

   μ₂/v - μ₁/u = (μ₂ - μ₁)/R

2. Put in numbers. 1.5/v + 1/100 = 0.5/20 = 1/40. So 1.5/v = 1/40 - 1/100 = 3/200, which gives v = +100 cm.
3. Locate the image. Positive v means a real image 100 cm inside the glass. The object is 100 cm in front of the surface, on the other side.
4. So. The distance from the object to the image is 100 + 100 = 200 cm.

The common slip: 100. Stopping at v = 100 cm gives 100, which is the image distance from the surface, not from the object.

The idea to keep. In single-surface refraction, u and v are always measured from the surface. If the question asks for the distance from the object, add the two distances across the surface.

Answer from the NTA final answer key. Solution by PrepWiser.