Question

A semiconductor laser emits light at 400.0 nm. The light is passed through a grating where 1,000 lines are etched covering a space of 10.00 mm. The light is directed directly at the grating.

What is the angle the light beam diffracts for first order diffraction?

a)15.24°
b)30.48°
c)45.72°
d)60.96°

Answer 1

The angle of first-order diffraction for the light beam passing through the grating is approximately 1.38°. The closest option among the given choices is a) 15.24°.

Step-by-step explanation:

Diffraction occurs when light waves pass through a narrow opening or encounter an object with regularly spaced lines or slits. In this case, the light emitted by the semiconductor laser passes through a grating with 1,000 lines covering a space of 10.00 mm. To calculate the angle of first-order diffraction, we can use the formula:

sin(θ) = mλ / d

Where θ is the angle of diffraction, m is the order of diffraction (in this case, 1), λ is the wavelength of light (400.0 nm or 4.00 × 10^-7 m), and d is the spacing between the lines on the grating (10.00 mm or 1.00 × 10^-2 m).

Plugging in the values, we have:

sin(θ) = (1)(4.00 × 10^-7) / (1.00 × 10^-2)

θ = arcsin((4.00 × 10^-7) / (1.00 × 10^-2))

Using a calculator to evaluate the arcsin, we find:

θ ≈ 0.024 radians ≈ 1.38°

Therefore, the angle of first-order diffraction for the light beam is approximately 1.38°. The correct answer is not provided in the options, but option a) 15.24° is closest to the correct answer.