Refraction at Spherical Surface and By Lenses

Every one of us has used the spherical lenses in some way or the other. The lens we use in spectacles, the mirror of our vehicle, is nothing but the spherical surface. But do you know what causes refraction in the spherical surface? Let us study in detail about spherical surface and also about refraction in lenses.

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Refraction at Spherical Surface

Let us now see the refraction of light at the spherical surface. Now, the change in direction or bending of a light wave passing from one transparent medium to another caused by the change in wave’s speed is the Refraction. Suppose the above figure is a spherical surface. There is one medium with refractive index n₁ and second medium with refractive index  n_2.

There is an object O and a ray of light from the object O is incident on the spherical mirror. Since it is moving from a rarer medium to a denser medium, the ray bends towards the normal.  An image is formed and radius of curvature of a spherical surface is R with the center C of the spherical surface.

Browse more Topics under Ray Optics And Optical Instruments

• Some Natural Phenomenon due to Sunlight
• Total Internal Reflection
• Reflection of Light by Spherical Mirrors
• Refraction
• Refraction Through a Prism
• Dispersion by a Prism
• Optical Instruments

• ”u” is the object distance from a pole of a spherical surface
• ”v” is the image distance from a pole of the spherical surface

Now as we know that,

• n₁ is the refractive index of a medium from which rays are incident.
• n₂ is the refractive index of another medium

We get,

• tanα = \( \frac{MN}{OM} \)
• tanγ = \( \frac{MN}{MC} \)
• tanβ = \( \frac{MN}{MI} \)

Now, for Δ NOC, i is the exterior angle.

i = ∠ NOM + ∠ NCM

i= \( \frac{MN}{OM} + \frac{MN}{MC} \) …….1

Similarly,

r =  \( \frac{MN}{MC} – \frac{MN}{MI} \) …….2

Now by using Snell’s law we get

n₁ sin i = n₂sin r

Substituting i and r from Eq. (1) and (2), we get

\( \frac{n_1}{OM} + \frac{n_2}{MI} = \frac{n_2-n_1}{MC} \)

As, OM = -u, MI = +v, MC = +R

Hence, the equation becomes \( \frac{n_2}{v} – \frac{n_1}{u} = \frac{n_2-n_1}{R} \)

Types of Lenses

1. Convex or Convergent Lenses
2. Concave or Divergent Lenses

A lens is a part of a transparent thick glass which is bounded by two spherical surfaces. It is an optical device through which the rays of light converge or diverge before transmitting. Thus spherical lenses are of two major kinds called Convex or Convergent lenses and Concave or Divergent lenses. The point from which these rays converge or appear to diverge is called the Focus or Focal point.

Convex or Convergent Lenses

A convex lens is thicker in the middle and thinner at the edges. A convex lens is also known as a “biconvex lens” because of two spherical surfaces bulging outwards.

 Concave or Divergent Lenses

A concave lens is thicker at the edges and thinner in the middle. A concave lens is also known as a “biconcave lens” because of two spherical surfaces bulging inwards

Ray diagrams for image formation by lenses

Lens Formula

Lens formula relates the image distance (v), object distance(u) and the focal length (f) of the lens.

\( \frac{1}{v} \) – \( \frac{1}{u} \) = \( \frac{1}{f} \)

Question For You

Q1. A fish sees the smiling face of a scuba diver through a bubble of air between them, as shown. Compared to the face of the diver, the image seen by the fish will be:

1. small and erect
2. smaller and inverted
3. larger and erect
4. larger and inverted

Answer: A. The image will be smaller and erect since the air bubble act as a concave lens which always forms smaller and erect images.