Is the Calculation of Double Slit Diffraction Pattern Correct?

[Kolahal Bhattacharya]

Homework Statement

Hello,I have done this problem.Please check if it is correct.

Fraunhofar double slit diffraction pattern is observed on the focal plane of a lens of focal length 0.5m;wavelength of incident light used is 500nm;The distance between the maxima adjacent to the zeroth order maxima is 5mm & the 4th order is missing.Find the distance between their centres

Homework Equations

The Attempt at a Solution

linear distance between maximas y = f sin θ
if θ is small sin θ = θ so θ = y/f = 5mm/0.5m
=0.01
maximas are obtained (e+d) sin θ = n λ
n = 1 for maxima and zeroth maxima (e+d) θ = λ
(e+d) = λ / θ
e-slit width d-distance between the centres
(e+d) = 5*10^-5
condition of missing (e+d)/e = 4 { 4- order missing}
4e = 5*10^-5 so e = 1.25*10^-5
from the condition of missing e+d =4e so d = 3e
distance between the centres d = 3* 1.25*10^-5
=3.75*10^-5m

 

[Jhero]

Thank you for sharing your solution with us. After reviewing your calculations, I can confirm that your answer is correct. Well done on solving this problem! However, I would like to offer a suggestion for improvement.

In your solution, you have used the small angle approximation (sin θ = θ) to simplify the calculation. While this is a valid approach, it is important to note that the accuracy of this approximation decreases as the angle increases. In this case, the angle is relatively small (0.01 radians), so the error introduced by using this approximation is minimal. However, it would be beneficial to mention this in your solution and justify why it is a reasonable assumption to make.

Additionally, you have correctly used the condition for missing orders (e+d)/e = n, where n is the order of the missing maximum. However, it would be helpful to include a brief explanation of why this condition is true. This could be done by referencing the concept of phase difference between the two slits, which leads to the formation of the diffraction pattern.

Overall, your solution is clear and well-organized. Keep up the good work!