Question

Unreasonable Results Red light of wavelength of 700 nm falls on a double slit separated by 400 nm.

(a) At what angle is the first-order maximum in the diffraction pattern?
(b) What is unreasonable about this result?
(c) Which assumptions are unreasonable or inconsistent?

Answer 1

The angle of the first-order maximum in the diffraction pattern for red light with a wavelength of 700 nm and a double slit separation of 400 nm is approximately 52.3°, which is unreasonable for a double slit diffraction pattern.

Step-by-step explanation:

The angle of the first-order maximum in the diffraction pattern for red light with a wavelength of 700 nm and a double slit separation of 400 nm can be calculated using the equation:

θ = sin^(-1)(mλ/d)

where θ is the angle, m is the order of the maximum (in this case it is the first-order maximum), λ is the wavelength of the light, and d is the separation between the double slits. Plugging in the values, we get:

θ = sin^(-1)(1 * 700 nm / 400 nm)

θ ≈ 52.3°

(b) The result is unreasonable because the angle of the first-order maximum is larger than what is physically possible for a double slit diffraction pattern. The maximum angle should typically be less than 10° for visible light.

(c) The assumption of using the formula for the angle of a first-order maximum is inconsistent because the result exceeds the expected range of values for a double slit diffraction pattern.