Question 1

What is θ_min for a monochromatic beam of light of wavelength 600 nm and an aperture diameter of 6.00 mm?

Accepted Answer

The formula for calculating the angular size of the diffraction pattern for a circular aperture is:

θ = 1.22λ/D

Where:
θ = angular size of the diffraction pattern
λ = wavelength of the light
D = diameter of the aperture

Plugging in the values given:
θ = 1.22(600 nm)/(6.00 mm) = 0.122 rad

Converting to degrees:
θ = 0.122 * (180/π) = 7.00°

Finally, expressing the answer in scientific notation:
θ = 7.00° = 7.00 * 10^(-2) rad = 122 * 10^(-3) rad

So the answer is C, 122 × 10^(-3) rad.

Question 2

What is the slit spacing of a diffraction necessary for a 600 nm light to have a first order principal maximum at 25.0°?

Accepted Answer

The slit spacing (d) can be found using the formula for diffraction maxima: d * sin(θ) = m * λ, where m is the order of the maximum (m=1 for first order), λ is the wavelength (600 nm = 600 x 10^-9 m), and θ is the angle (25.0°). Solving for d gives approximately 1.42 μm.

Question 3

What is the limiting angle of resolution for the eye if the pupil diameter of the eye is 4.0 mm, a wavelength of light of 600 nm and index of refraction for the eye equal to 1.34?

Accepted Answer

The formula for the limiting angle of resolution is:

θ = 1.22 × λ / (D × n)

where θ is the limiting angle of resolution in radians, λ is the wavelength of light, D is the diameter of the pupil, and n is the index of refraction of the eye.

Plugging in the given values, we get:

θ = 1.22 × 600 nm / (4.0 mm × 1.34) = 1.4 × 10^-4 rad

Therefore, the limiting angle of resolution for the eye is 1.4 × 10^-4 rad, which corresponds to choice C.

Question 4

A monochromatic beam of light of wavelength 600 nm is incident normally on a diffraction grating with a slit spacing of 1.70 × 10^-⁴ cm. What is the angle for the first order maximum?

Accepted Answer

The answer of A monochromatic beam of light of wavelength...

Question 5

A single slit, which is 0.050 mm wide, is illuminated by light of 550 nm wavelength. What is the angular separation between the first two minima on either side of the central maximum?

Accepted Answer

The angular position of the minima in a single-slit diffraction pattern is given by the formula θ = mλ/a, where m is the order of the minimum, λ is the wavelength, and a is the slit width. For the first minima (m=1), θ = (1)(550 x 10^-9 m) / (0.050 x 10^-3 m) = 0.011 radians. Converting to degrees, θ ≈ 0.63°. The angular separation between the first two minima on either side is 2θ, which is approximately 0.63°.

Question 6

In a single-slit diffraction experiment, a beam of monochromatic light of wavelength 630 nm is incident on a slit of width 0.400 mm. If the distance between the slit and the screen is 1.80 m, what are the positions of the first dark fringes?

Accepted Answer

The answer of In a single-slit diffraction experiment, a beam...

Question 7

Light of wavelength 687 nm is incident on a single slit 0.75 mm wide. At what distance from the slit should a screen be placed if the second dark fringe in the diffraction pattern is to be 1.7 mm from the center of the screen?

Accepted Answer

The position of the dark fringes in a single-slit diffraction pattern is given by the formula $ a \sin \theta = m \lambda $, where $ a $ is the slit width, $ \lambda $ is the wavelength, $ m $ is the order of the dark fringe, and $ \theta $ is the angle. For small angles, $ \sin \theta \approx \tan \theta = \frac{y}{L} $, where $ y $ is the fringe distance from the center and $ L $ is the distance to the screen. For the second dark fringe ($ m = 2 $), $ a \frac{y}{L} = 2 \lambda $. Solving for $ L $ gives $ L = \frac{a y}{2 \lambda} $. Substituting $ a = 0.75 \times 10^{-3} $ m, $ y = 1.7 \times 10^{-3} $ m, and $ \lambda = 687 \times 10^{-9} $ m, we find $ L \approx 0.93 $ m.

Question 8

A certain astronomical telescope has a diameter of 5.60 m. What is the minimum angle of resolution for this telescope at a wavelength of 620 nm?

Accepted Answer

The minimum angle of resolution is given by the formula:
θ = 1.22λ/D
where θ is the minimum angle of resolution,
λ is the wavelength of light, and
D is the diameter of the telescope.
Plugging in the given values, we get:
θ = 1.22 x 620 nm / 5.60 m
θ = 1.35 × 10^-7 rad
Therefore, the correct answer is D.

Question 9

Light of wavelength 580 nm is incident on a slit of width 0.300 mm. An observing screen is placed 2.00 m from the slit. Find the width of the central maximum.

Accepted Answer

The width of the central maximum in a single-slit diffraction pattern is given by the formula: $ W = \frac{2 \lambda L}{a} $, where $ \lambda $ is the wavelength, $ L $ is the distance to the screen, and $ a $ is the slit width. Substituting the given values: $ W = \frac{2 \times 580 \times 10^{-9} \times 2}{0.300 \times 10^{-3}} \approx 7.7 $ mm.

Question 10

The limiting angle of resolution for the eye is 1.4 × 10^-⁴ rad. What is the minimum separation between two point sources of light that the eye can distinguish if they are at a distance of 40 m from the observer?

Accepted Answer

The answer of The limiting angle of resolution for the...

Question 11

Light of wavelength 580 nm is incident on a slit of width 0.300 mm. An observing screen is placed 2.00 m from the slit. Find the position of the first order dark fringe from the center of the screen.

Accepted Answer

The answer of Light of wavelength 580 nm is incident...

Question 12

In a single-slit diffraction experiment, a beam of monochromatic light of wavelength 630 nm is incident on a slit of width 0.400 mm. If the distance between the slit and the screen is 1.80 m, what is the width of the central bright fringe?

Accepted Answer