What is the formula for the maximum number of orders visible?

The maximum order $n_{max}$ is found by setting $\theta = 90^{\circ}$, so $\sin \theta = 1$. Thus, $n_{max} = d/\lambda$. The result must be rounded down to the nearest integer.

What is the relationship between the number of lines per mm ($N$) and the slit spacing ($d$)?

The slit spacing $d$ is the reciprocal of the number of lines per unit length. Specifically, $d = 1/N$. If $N$ is in lines/mm, you must multiply by 1000 to get lines/m before calculating $d$ in meters.

How does the interference pattern of a diffraction grating differ from a double-slit pattern?

A diffraction grating produces much sharper and narrower bright fringes with large dark regions in between. This is because the constructive interference from many slits is much more restrictive than from only two slits.

Why is the small-angle approximation ($\sin \theta \approx \tan \theta$) usually avoided in diffraction grating experiments?

Diffraction gratings typically produce large angles of diffraction (often $> 10^{\circ}$). At these angles, the difference between $\sin \theta$ and $\tan \theta$ becomes significant, leading to inaccuracies in the calculated wavelength.

What is a common systematic error when measuring the distance $h$ to the fringes?

Parallax error is common if the ruler is not placed directly against the screen or if the observer's eye is not level with the fringe. Using a set square to ensure the screen is perpendicular to the beam also helps prevent systematic geometric errors.

What happens to the percentage uncertainty of $h$ if you use a grating with fewer lines per mm?

The percentage uncertainty increases. Fewer lines per mm means a larger $d$, which results in a smaller diffraction angle $\theta$ and a smaller distance $h$. A smaller $h$ measured with the same ruler resolution leads to a higher percentage uncertainty.

Why might a student fail to see any second-order maxima on the screen?

This occurs if the required angle for $n=2$ exceeds $90^{\circ}$. Mathematically, if $\frac{n\lambda}{d} > 1$, that order cannot exist. This happens if the wavelength is too long or the slit spacing $d$ is too small.

Define the 'order' ($n$) in the diffraction grating equation.

The order $n$ is an integer representing the number of wavelengths of path difference between light from adjacent slits. $n=0$ is the central maximum, $n=1$ is the first bright fringe on either side, and so on.

How do you calculate the angle $\theta$ from experimental measurements of $h$ and $D$?

Use the inverse tangent function: $\theta = \tan^{-1}(h/D)$. Here, $h$ is the distance from the center to the $n$-th order fringe, and $D$ is the distance from the grating to the screen.

Why does a laser provide a better pattern than a standard light bulb for this experiment?

A laser is monochromatic (single wavelength) and coherent. A standard bulb emits a spectrum of wavelengths which would each diffract at different angles, creating a blurred rainbow effect rather than distinct sharp spots.

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5. Waves & Particle Nature of Light

Core Practical 8: Investigating Diffraction Gratings

Summary

This practical methodology focuses on determining the wavelength of monochromatic light by analyzing the interference patterns produced by a diffraction grating. By measuring the angular displacement of various orders of maxima, the diffraction grating equation can be applied to calculate the wavelength with high precision.

1. Core Concepts & Experimental Aim

Objective: The primary goal is to use a diffraction grating to determine the wavelength ( $\lambda$ ) of a laser light source by measuring the spacing of interference fringes on a distant screen.
Diffraction Grating: A device consisting of a large number of equally spaced parallel slits. When light passes through, it diffracts and interferes, creating a pattern of bright spots known as maxima.
Monochromatic Light: The experiment requires a single-wavelength source, typically a laser, to ensure the interference pattern is sharp and the maxima are well-defined for measurement.

Geometric setup of a diffraction grating experiment showing the laser path, grating, screen distance D, fringe height h, and diffraction angle theta.

2. Underlying Principles

3. Methodology & Data Collection

4. Mathematical Analysis

5. Key Distinctions

6. Exam Strategy & Tips