Determine the wavelength of light emitted by a Helium-Neon laser and the grating element of a plane diffraction grating using a simple geometric method.
To determine the wavelength of light emitted by a Helium-Neon (He-Ne) laser using a plane diffraction grating, and to determine the number of lines per unit length (grating element) of the grating.
Diffraction is the bending and spreading of light waves as they pass through a narrow opening or around an obstacle whose size is comparable to the wavelength of light. A diffraction grating consists of a large number of closely spaced, equally ruled parallel slits (typically hundreds to thousands per millimetre). When a parallel, monochromatic beam of light falls on such a grating, each slit acts as a source of secondary wavelets (Huygens’ principle). These wavelets interfere constructively at certain specific angles, producing a series of sharp, bright spots called principal maxima on a screen placed beyond the grating, with a bright central maximum (zero order) and symmetric higher-order maxima on either side.
d sinθ = nλ
where:
The grating element d is the distance between the centres of two consecutive slits (or lines) on the grating. It is related to N, the number of lines ruled per unit length of the grating (usually specified by the manufacturer, e.g., in lines per millimetre or lines per inch), by:
d = 1 / N
For example, a grating ruled with N = 600 lines/mm has a grating element d = 1/600 mm = 1666.7 nm.
A He-Ne laser emits light that is highly monochromatic (a single, well-defined wavelength), coherent (constant phase relationship across the beam), and well-collimated (travels as a narrow, nearly parallel beam with negligible divergence). Because of these properties, the diffraction maxima produced by a laser are exceptionally sharp, bright, and well-separated, unlike the broader, weaker fringes obtained with ordinary extended sources. This makes the grating method a very precise way of determining the laser’s wavelength, and also allows a simple geometric (non-spectrometer) measurement technique to be used, since the beam and the diffracted orders travel in well-defined straight lines to a distant screen.
Diffraction is a wave phenomenon in which light bends and spreads around obstacles or through narrow slits within the same medium, without any change in the speed of light. Refraction, on the other hand, is the bending of a light ray that occurs specifically because its speed changes as it crosses the boundary between two different media (e.g., air to glass). Diffraction depends on wavelength and slit/obstacle size, while refraction depends on the refractive indices of the two media and the angle of incidence.
Figure: Experimental setup showing the He-Ne laser beam incident on the plane diffraction grating, producing a central maximum (n = 0) and first-order maxima (n = 1) on the screen, with the grating-to-screen distance L and the lateral offset x used to find θ = tan⁻¹(x/L).
Grating used: N = 600 lines/mm, so grating element d = 1/600 mm = 1666.7 nm.
| S.No. | L (cm) | Order n | x (cm) | tanθ = x/L | θ (°) | sinθ | λ = d sinθ/n (nm) |
|---|---|---|---|---|---|---|---|
| 1 | 100.0 | 1 | 41.0 | 0.4100 | 22.29 | 0.3793 | 632.2 |
| 2 | 100.0 | 1 | 41.1 | 0.4110 | 22.34 | 0.3801 | 633.5 |
| 3 | 150.0 | 1 | 61.6 | 0.4107 | 22.32 | 0.3798 | 633.0 |
| 4 | 150.0 | 1 | 61.7 | 0.4113 | 22.36 | 0.3804 | 634.0 |
| 5 | 80.0 | 2 | 93.4 | 1.1675 | 49.41 | 0.7591 | 632.6 |
Mean λ = (632.2 + 633.5 + 633.0 + 634.0 + 632.6) / 5 ≈ 633.1 nm
Given:
Step 1 — Find the angle of diffraction:
tanθ = x / L = 41.0 / 100.0 = 0.4100
θ = tan⁻¹(0.4100) = 22.29°
Step 2 — Apply the grating equation:
λ = d sinθ / n
λ = 1666.7 × sin(22.29°) / 1
λ = 1666.7 × 0.3793
λ ≈ 632.2 nm
This value is in excellent agreement with the standard (known) wavelength of He-Ne laser light, 632.8 nm. Taking the mean of all five readings gives a value of 633.1 nm, which is within experimental error of the accepted value.
The experimentally determined wavelength of the He-Ne laser light:
λ = 632.8 ± 2 nm
This closely matches the standard value of 632.8 nm (red light) for a Helium-Neon laser, confirming the wave nature of light through the phenomenon of diffraction.
A diffraction grating is an optical device consisting of a very large number of closely spaced, equally ruled parallel slits (or lines) on a transparent or reflective surface. When a beam of light passes through the grating, each slit acts as a source of secondary wavelets that interfere with one another. Constructive interference occurs at specific angles satisfying d sinθ = nλ, producing sharp, well-separated bright fringes called principal maxima on a screen placed beyond the grating.
A laser produces highly monochromatic, coherent, and well-collimated light, meaning all the light waves have nearly the same wavelength, a constant phase relationship, and travel as a narrow parallel beam. This produces sharp, bright, and well-defined diffraction maxima with minimal spreading, making the angle and distance measurements far more accurate than would be possible with an ordinary, non-coherent, broad-spectrum light source such as a sodium lamp.
The grating element, denoted d, is the distance between the centres of two adjacent slits (or lines) on the grating. It is the reciprocal of N, the number of lines ruled per unit length of the grating, so d = 1/N. For example, a grating with 600 lines per millimetre has a grating element d = 1/600 mm = 1666.7 nanometres, which directly enters the grating equation used to calculate wavelength.
A laser beam is a highly concentrated, collimated, and coherent source of light energy that the eye’s lens focuses onto an extremely small spot on the retina, delivering a very high energy density. Even a low-power He-Ne laser can cause permanent retinal damage or blindness if viewed directly or via a specular reflection, because unlike ordinary light, the beam does not spread out and lose intensity over short distances, so proper laser safety precautions must always be followed.
Diffraction is the bending and spreading of waves as they pass through a narrow slit or around an obstacle, occurring within the same medium without any change in speed. Refraction, in contrast, is the bending of a wave’s path caused by a change in its speed as it crosses a boundary between two different media. Interference is the superposition of two or more coherent waves; diffraction can actually be viewed as the interference of an infinite (or very large) number of secondary wavelets originating from different points across a single slit or grating.
