Prism Instruments

9.6 Refraction Through a Prism

A prism is a triangular block of transparent material. Light entering through one of its two refracting faces leaves through the other, being bent twice towards the base. The angle between the two refracting faces is the angle of prism \(A\); the angle between the emergent ray and the original direction of the incident ray is the angle of deviation \(\delta\).

Minimum Deviation

As the angle of incidence varies, \(\delta\) first decreases, reaches a minimum \(\delta_m\), then increases. At this minimum, the ray inside the prism travels parallel to the base and the path is symmetric: \(i = e\) and \(r_1 = r_2 = A/2\). This gives the prism formula for refractive index:

9.7 Dispersion by a Prism

When white light passes through a prism it emerges as a band of seven colours — Violet, Indigo, Blue, Green, Yellow, Orange, Red (VIBGYOR). This splitting is called dispersion and arises because the refractive index of the glass depends on wavelength: shorter wavelengths (violet) experience a higher \(n\) and are bent more; longer wavelengths (red) experience a smaller \(n\) and are bent less.

9.8 Some Natural Phenomena Due to Refraction and Scattering

Rainbow

A rainbow is nature's own giant spectrum, produced when sunlight enters a spherical raindrop, undergoes refraction → internal reflection → refraction. The primary rainbow appears at ~42° from the anti-solar point with red on the outside and violet on the inside; the fainter secondary rainbow appears at ~51° with reversed colour order (two internal reflections).

Scattering of Light

When light encounters particles much smaller than its wavelength, it is scattered. Lord Rayleigh showed that the scattered intensity varies as

This inverse-fourth-power law explains:

• Blue sky: Blue light (\(\lambda \approx 450\) nm) scatters about 10 times more strongly than red (\(\lambda \approx 700\) nm) by air molecules, so the diffuse sky glow looks blue.
• Red sun at sunrise/sunset: At low elevations, sunlight traverses a much longer atmospheric path. Blue is scattered out along the way, so the direct beam that reaches us is dominated by the red-orange end.
• White clouds: Cloud droplets are much larger than the wavelength of visible light. All colours are scattered almost equally (Mie scattering), so clouds look white.

9.9 Optical Instruments

The Human Eye

The eye acts as a fixed camera with a variable-focus lens. Ciliary muscles alter the focal length of the eye-lens to focus objects at different distances — a process called accommodation. The near point (least distance of distinct vision) for a normal young adult is \(D = 25\) cm.

Simple Microscope (Magnifying Glass)

A convex lens with the object placed within its focal length produces a virtual, erect, magnified image.

Compound Microscope

Two converging lenses: a short-focus objective (\(f_o\)) forms a real, inverted, magnified intermediate image, which is then magnified further by an eyepiece (\(f_e\)) acting as a simple magnifier.

where \(L\) is the distance between the objective's second focus and the eyepiece's first focus (the tube length).

Astronomical (Refracting) Telescope

Objective has a long focal length and large aperture, the eyepiece a short focal length. In normal adjustment (final image at infinity):

Reflecting Telescope (Cassegrain)

A large concave primary mirror replaces the objective lens. A small convex secondary mirror redirects the converging beam through a hole in the primary to the eyepiece. Advantages over refractors: no chromatic aberration, easier to support huge apertures, and cheaper to build large (most modern professional telescopes — Hubble, Palomar — are reflecting).

Worked Examples — Prism, Eye and Instruments