衍射：練習題

How does increasing the width of a single slit affect the width of the central maximum in its diffraction pattern, assuming monochromatic light is used?

Which characteristic best distinguishes the interference pattern produced by a diffraction grating (many slits) from the diffraction pattern produced by a single slit?

White light is incident normally on a diffraction grating. Which of the following statements correctly describes the first-order spectrum produced?

In the diffraction grating equation \(d \sin \theta = n\lambda\) , what quantity does the integer \(n\) represent?

Monochromatic light of wavelength \(\lambda_1\) is incident upon a single slit. This light is then replaced by monochromatic light of wavelength \(\lambda_2\) , where \(\lambda_2 > \lambda_1\) . If all other factors remain constant, how does the resulting diffraction pattern change?

In single-slit diffraction, what happens to the angular width of the central maximum if the width of the slit is increased while keeping the wavelength of the monochromatic light constant?

A diffraction grating has \(4.0 \times 10^5\) lines per metre. Calculate the angular separation between the first-order and second-order maxima when monochromatic light of wavelength \(600 \text{ nm}\) is incident normally on the grating.

A plane diffraction grating is illuminated normally by a white light source producing wavelengths ranging from \(400\text{ nm}\) to \(700\text{ nm}\) . Determine the minimum integer order, \(n\), for which the angular deviation of the spectrum of order \(n+1\) begins to overlap with the angular deviation of the spectrum of order \(n\) .

A diffraction grating has \(4.50 \times 10^5\) lines per metre. Monochromatic light of wavelength \(532\, \text{nm}\) is incident normally on the grating.

a) Calculate the grating spacing, \(d\), in metres.
b) Calculate the angular separation between the first-order and the second-order principal maxima.
c) State the effect on the positions of the maxima if the grating is replaced with one having more lines per millimetre.

A beam of monochromatic blue light is incident normally on a narrow single slit of width \(a\). A diffraction pattern consisting of a bright central maximum and fainter secondary maxima and minima is observed on a screen placed far away.

a) State the condition for the formation of the first diffraction minimum in terms of slit width \(a\), wavelength \(\lambda\), and angle \(\theta\) relative to the central maximum. (1 point)

b) Explain qualitatively how the width of the central maximum changes if the following changes are made, assuming all other parameters remain constant:

i. The blue light is replaced by monochromatic red light (which has a longer wavelength). (2 points)

ii. The width of the slit \(a\) is reduced. (2 points)