Ray Optics — Part 2: Spherical surfaces, lenses and the prism: visual lesson, CBSE Class 12 Physics

Lesson

Spherical surfaces, lenses and the prism

Part 2 — from one curved surface to a thin lens, combinations of lenses, and the prism.

In this lesson you will

Derive refraction at a spherical surface and the lens maker’s formula
Apply the thin lens formula, magnification and the power of lenses in contact
Derive the relation for the angle of minimum deviation of a prism

Diagram

Refraction at a spherical surface

For a point object in medium $n_1$ and a spherical surface of radius $R$ bounding medium $n_2$ (paraxial rays, sign convention from the pole): $\dfrac{n_2}{v} - \dfrac{n_1}{u} = \dfrac{n_2 - n_1}{R}$

Derivation: apply Snell’s law (small angles) at the point where a ray meets the surface, and relate the angles to u, v and R.

Worked example

Worked example 4: an image inside glass

A point object in air is 30 cm in front of a convex glass surface ( $n = 1.5$ , $R = +10$ cm). Where is the image?

Step 1 — $\dfrac{1.5}{v} - \dfrac{1}{-30} = \dfrac{1.5 - 1}{10} = 0.05$ .
Step 2 — $\dfrac{1.5}{v} = 0.05 - \dfrac{1}{30} \approx 0.0167$ , so $v \approx 90$ cm.
Step 3 — positive: a real image 90 cm inside the glass.

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