Question

(a) How wide is a single slit that produces its first minimum for 633-nm light at an angle of 28.0º?

(b) At what angle will the second minimum be?
a) (a) 1.00 μm, (b) 56.0º
b) (a) 2.00 μm, (b) 28.0º
c) (a) 0.50 μm, (b) 84.0º
d) (a) 4.00 μm, (b) 14.0º

Answer 1

The width of the single slit cannot be determined without the distance from the screen to the slit. The angle of the second minimum for a single slit can be calculated using the formula Angle2 = Angle1 / (n + 1), where Angle1 is the angle of the first minimum and n is the order of the minimum.

Step-by-step explanation:

(a) How wide is a single slit that produces its first minimum for 633-nm light at an angle of 28.0°?

The width of a single slit can be calculated using the formula:

Width = (wavelength / angular width) * (distance from screen to slit)

Here, the wavelength is 633 nm (or 6.33 × 10-7 m), the angular width is 28.0° (or 0.49 rad), and the distance from screen to slit is not given. Therefore, it is not possible to calculate the width of the single slit without the distance from the screen to the slit.

(b) At what angle will the second minimum be?

The angle of the second minimum can be calculated using the formula:

Angle2 = Angle1 / (n + 1)

Here, Angle1 is 28.0° and n is 1 (since it is the first minimum). Therefore, the angle of the second minimum will be:

Angle2 = 28.0° / (1 + 1) = 14.0°