Q: A single slit of width $$0.02\ \mathrm{mm} is $$illuminated by light of wavelength $$500\ \mathrm{nm}. $$What is the angular position of the first minimum in the diffraction pattern?

$$\theta = \arcsin\left(\frac{500 \times 10$$^{-9}$$}{0.02 \times 10$$^{-3}$$}\right)$$

Q: A telescope has a primary mirror of diameter $$2.0\ \mathrm{m}$$ and observes light of wavelength $$600\ \mathrm{nm}. $$What is the minimum angular separation it can resolve according to the Rayleigh criterion?

$$\theta = \frac{1.22 \times 600 \times 10$$^{-9}$$}{2.0}$$

Q: A diffraction grating has $$10,000$$ lines per cm. What is the spacing $$d$$ between adjacent lines?

$$d = \frac{1}{10,000}\ \mathrm{cm} = 1 \times 10$$^{-4}$$\ \mathrm{cm}$$

Q: If the diameter of your pupil is $$3.0\ \mathrm{mm}$$ and you are observing light of wavelength $$550\ \mathrm{nm}$$, what is the minimum angular separation you can resolve?

$$\theta = \frac{1.22 \times 550 \times 10$$^{-9}$$}{3.0 \times 10$$^{-3}$$}$$

Question 1

A single slit of width $$0.02\ \mathrm{mm} is $$illuminated by light of wavelength $$500\ \mathrm{nm}. $$What is the angular position of the first minimum in the diffraction pattern?

Accepted Answer

$$	heta = \arcsin\left(\frac{500 	imes 10$$^{-9}$$}{0.02 	imes 10$$^{-3}$$}ight)$$

Question 2

Which statement best describes the effect of increasing the number of slits in a diffraction grating?

Accepted Answer

The maxima become narrower and more intense.

Question 3

A telescope has a primary mirror of diameter $$2.0\ \mathrm{m}$$ and observes light of wavelength $$600\ \mathrm{nm}. $$What is the minimum angular separation it can resolve according to the Rayleigh criterion?

Accepted Answer

$$	heta = \frac{1.22 	imes 600 	imes 10$$^{-9}$$}{2.0}$$

Question 4

Which type of spectrum is produced when light from a hot, dense object passes through a cool, thin gas?

Accepted Answer

Absorption (dark line) spectrum

Question 5

In a single-slit diffraction experiment, the width of the central maximum on a screen $$L$$ meters away is given by which expression?

Accepted Answer

$$w = \frac{2 \lambda L}{D}$$

Question 6

A diffraction grating has $$10,000$$ lines per cm. What is the spacing $$d$$ between adjacent lines?

Accepted Answer

$$d = \frac{1}{10,000}\ \mathrm{cm} = 1 	imes 10$$^{-4}$$\ \mathrm{cm}$$

Question 7

Which equation gives the condition for constructive interference (principal maxima) in a diffraction grating?

Accepted Answer

$$d \sin 	heta = m \lambda$$

Question 8

A microscope objective has a focal length $$f$$ and diameter $$D. $$What is the resolving power $$RP in $$radians for an object at the focal point?

Accepted Answer

$$RP = \frac{1.22 \lambda f}{D}$$

Question 9

Which of the following best explains why X-ray diffraction is used to study crystal structures?

Accepted Answer

The spacing between atomic planes in crystals is comparable to X-ray wavelengths.

Question 10

Bragg's law for X-ray diffraction is given by which equation?

Accepted Answer

$$2d \sin 	heta = m \lambda$$

Question 11

If the diameter of your pupil is $$3.0\ \mathrm{mm}$$ and you are observing light of wavelength $$550\ \mathrm{nm}$$, what is the minimum angular separation you can resolve?

Accepted Answer

$$	heta = \frac{1.22 	imes 550 	imes 10$$^{-9}$$}{3.0 	imes 10$$^{-3}$$}$$

Question 12

Which of the following statements about the central maximum in a single-slit diffraction pattern is correct?

Accepted Answer

It is twice as wide as the other maxima and much brighter.

Question 13

A spectrometer is used to measure the wavelength of light by analyzing the angle of diffraction. Which formula is used for this measurement?

Accepted Answer

$$d \sin 	heta = m \lambda$$

Question 14

In a single-slit diffraction experiment, which condition must be met for a dark band (minimum) to appear on the screen?

Accepted Answer

$$D \sin 	heta = m \lambda$$

Question 15

Which of the following is NOT a type of spectrum observed in spectroscopy?

Accepted Answer

Discrete spectrum

Question 16

A microscope lens typically cannot resolve details smaller than which value?

Accepted Answer

$$\frac{\lambda}{2}$$

Question 17

Which physical principle explains the formation of concentric bright and dark rings in the diffraction pattern of a circular aperture?

Accepted Answer

Huygens' principle

Question 18

If a diffraction grating is used to separate white light, what is observed?

Accepted Answer

A series of colored spectra (rainbow patterns) at different angles

Question 19

Which of the following best describes the Rayleigh criterion for resolution?

Accepted Answer

Two images are just resolvable when the center of one diffraction pattern is directly over the first minimum of the other.

Chapter 35: Diffraction and Polarization – Study Notes

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