Optics Bench · OpticsLab

Law of Reflection

A laser shines along the protractor disk toward the center O of a plane mirror. Through the point of incidence, draw the normal perpendicular to the mirror (the vertical dashed line on the disk). The angle between the incident ray and the normal is the angle of incidence i; the angle between the reflected ray and the normal is the angle of reflection r.

r = i

The reflected ray, the incident ray and the normal lie in the same plane, and the reflected and incident rays are on opposite sides of the normal.

Drag the laser pointer around the disk, or use the slider to change the angle of incidence, and press Record to save each pair of i and r. If light is sent back along the reflected ray, it leaves along the original incident ray: light paths are reversible.

Plane Mirror Images

Use a transparent glass plate in place of a plane mirror: you can see both the image of the lit candle A behind the glass and the candle B that is actually behind the glass.

Drag the unlit candle B until it coincides exactly with the image of A from every viewing angle, as if B were lit too. Then measure:

image distance = object distance, image height = object height

A plane mirror forms an upright, same-size virtual image, symmetric to the object about the mirror. Turn on the light paths: the backward extensions of the reflected rays meet at the image point, but no real light converges there, so the image is virtual. Place a screen there and nothing appears on it.

Refraction of Light

A laser travels obliquely from air into the center of the flat face of a semicircular glass block. Inside the glass the light bends toward the normal, so the angle of refraction r is smaller than the angle of incidence i. It leaves through the curved face along a radius without bending again, which makes reading easy.

Measure several pairs of i and r: i and r are not proportional, but their sines are. This is the law of refraction:

n = sin i / sin r

n is the refractive index of the medium. Plot sin i against sin r in the data dock; the slope is n. Switch to water (1.33) or diamond (2.42) to compare.

Total Internal Reflection & Optical Fibers

When light goes from glass into air, the angle of refraction is larger than the angle of incidence. As the angle of incidence increases, the refracted ray moves closer to the surface and grows dimmer, while the reflected ray grows brighter.

When the angle of incidence reaches the critical angle C, the angle of refraction is 90°. Beyond it, the refracted ray disappears completely and only reflected light remains. This is total internal reflection:

sin C = 1 / n

The critical angle of glass is about 41°, but diamond's is only 24°, which is why diamonds sparkle so much. Switch to the optical fiber: light totally reflects again and again at the core–cladding boundary, so it comes out of the other end even when the fiber is bent.

Prism Dispersion

A beam of white light passing through a triangular prism spreads out on the screen into a band of red, orange, yellow, green, blue, indigo and violet. This is dispersion. Newton used this experiment to show that white light is a mixture of many colors.

The same glass has a different refractive index for each color: violet has the largest index and bends the most; red has the smallest and bends the least.

Switch to a single-color red laser: after the prism it only bends and no longer splits. Add an inverted prism behind it, and the colors recombine into white light.

Convex Lens Imaging

Place the candle, convex lens and screen in order on the optical bench, with the centers of the flame, lens and screen at about the same height. Move the screen until the image on it is sharpest, then read the object distance u and image distance v.

· u > 2f: inverted, diminished real image (camera)· u = 2f: inverted, same-size real image· f < u < 2f: inverted, magnified real image (projector)· u = f: no image· u < f: upright, magnified virtual image (magnifying glass), which cannot be caught on the screen

1/u + 1/v = 1/f

Record several pairs of u and v and plot 1/u against 1/v in the data dock; the intercept is 1/f.

The Eye & Vision Correction

The eye works like a camera: the crystalline lens acts as a convex lens and the retina acts as the screen. The ciliary muscles change the thickness (focal length) of the lens so that objects near and far all form sharp images on the retina.

Nearsighted (myopic) eye: the eyeball is too long (or the lens too thick), so images of distant objects fall in front of the retina and distant things look blurry. It is corrected with a concave lens, which spreads the light out a little.

Farsighted (hyperopic) eye: images fall behind the retina and near things look blurry. It is corrected with a convex lens.

prescription (×100) = optical power × 100 = 100 / f (f in m)

Double-Slit Interference

A laser falls on two very close slits, which act as two coherent sources. The two light waves superpose on the screen: where the path difference is a whole number of wavelengths they reinforce, giving bright fringes; where it is an odd number of half wavelengths they cancel, giving dark fringes.

Δx = L λ / d

The spacing Δx between adjacent bright fringes is proportional to the screen distance L and the wavelength λ, and inversely proportional to the slit separation d. The colored ripples on the bench illustrate the superposition of the two waves (wavelength exaggerated).

Measure the total width of n bright fringes with the measuring eyepiece to calculate the wavelength. With white light, the central fringe is white and colored fringes appear on both sides.

Single-Slit Diffraction & Gratings

After light passes through a very narrow single slit, the screen shows a wide, bright central fringe with narrower, dimmer fringes on each side. This is diffraction. The narrower the slit, the wider the central fringe and the more obvious the diffraction.

central fringe half-width x₁ = L λ / a

Unlike double-slit fringes (equally spaced), in single-slit diffraction the central bright fringe is twice as wide as the others.

A diffraction grating has a large number of equally spaced slits, giving very sharp, bright principal maxima: d sinθ = kλ. With white light each order becomes a colored spectrum, with violet deviated least and red most: exactly the opposite of a prism.

Thin-Film Interference

Lift a wire loop out of soap solution and hold it upright. Gravity makes the film thin at the top and thick at the bottom. Light reflects from the front and back surfaces of the film, and the two reflected waves superpose: where the thickness t satisfies 2nt ≈ kλ they cancel; where 2nt ≈ (k + ½)λ they reinforce.

Each thickness corresponds to one color, so horizontal colored bands appear. As the film keeps thinning, the bands move downward and the very top turns black, and then the film bursts. Under yellow sodium light you see only alternating yellow and black bands.

Newton's rings: a plano-convex lens rests on a flat glass plate. The air film thickness is t = r²/2R, forming concentric rings that are widely spaced in the center and crowded toward the edge:

rk = √(kλR)

Polarization of Light

Light is a transverse wave. Unpolarized (natural) light vibrates in all directions in the plane perpendicular to its direction of travel. After passing through a polarizer, only the light vibrating along the transmission axis remains: linearly polarized light, at half the intensity.

Look through a second polarizer (the analyzer): as you rotate the analyzer, the transmitted intensity changes periodically, and the light is completely blocked when the two transmission axes are perpendicular. Malus's law:

I = I₀ cos²θ

Liquid-crystal displays: twisted liquid crystal sits between two crossed polarizers. The liquid crystal rotates the polarization by 90°, so light gets through (bright). With voltage applied, the molecules line up vertically and no longer rotate it, so the light is blocked (dark).

Free Optics Bench

All geometric optics components are available: laser, white light source, plane mirror, convex lens, concave lens, semicircular block, rectangular block, triangular prism and screen.

· Click the buttons on the panel to add components· Drag a component to move it; drag the gold ring above it to rotate it· Select one and press Delete to remove it

Try building a periscope or a telescope, or make a beam bounce back and forth between several mirrors.