Question

In a Fraunhofer N-slit diffraction experiment, a grating has $5000$ lines/cm, and monochromatic light of wavelength $5 \times 10^{-5}$ cm is used. What is the highest order spectrum that may be observed?

• A. 1
• B. 2
• C. 3
• D. 4

Hint:

For a diffraction grating, sin θ ≤ 1 =⇒ n λ ≤ d. The maximum observable integer n is ⌊d/λ⌋.

Answer 1

The Correct Option is D

The grating equation:
\[d \sin \theta = n \lambda, \quad (\sin \theta \leq 1).\]
Here, \(d = \frac{1}{5000} \, \text{cm} = 2 \times 10^{-4} \, \text{cm}\), \(\lambda = 5 \times 10^{-5} \, \text{cm}\). Thus,
\[n \lambda \leq d \implies n \leq \frac{d}{\lambda} = \frac{2 \times 10^{-4}}{5 \times 10^{-5}} = 4.\]
Hence the highest integer order is \(n = 4\).