Distance between two second order maxima

In summary, we can use the equation d sinθ = mλ to find the distance between the two second-order maxima when monochromatic light strikes a diffraction grating at normal incidence before illuminating a screen 1.99 m away. By setting m = 2, we can use the same value for lambda/d that we found when calculating the first-order maxima. Using this value and the equation again, we can find the angle theta and use trigonometry to determine the distance between the two second-order maxima.
  • #1
kuzco890
4
0

Homework Statement


Monochromatic light strikes a diffraction grating at normal incidence before illuminating a screen 1.99 m away. If the first-order maxima are separated by 1.36 m on the screen, what is the distance between the two second-order maxima?


Homework Equations


I think these are the relevant equations:
deltaL = dsinθ
y = Ltanθ


The Attempt at a Solution


L = 1.99 m
I'm not sure where the 1.36 and 1.99 come in.
 
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  • #3
So I only need the d sinθ = mλ equation?
Would you be able to help walk me through it?
I feel like I need the y = Ltanθ or deltaL = dsinθ equation.
Doesn't L = 1.36 for the first order maxima?
d = 1.99 m
m = 2?
 
  • #4
Draw the triangle with theta, x (distance from center to maximum - half the 1.36), L (L is the hypotenuse), and the 1.99 m distance to the screen. Use the triangle and some trig to find theta.

Use the formula to find lambda/d. This value doesn't change as you move to 2nd order, so you can use the formula again with this value to find theta when m = 2.
 
  • #5
Thanks!
 

Related to Distance between two second order maxima

What is meant by "Distance between two second order maxima"?

The distance between two second order maxima refers to the spacing between the second bright fringes in a double-slit interference pattern. This distance is measured from the center of one bright fringe to the center of the adjacent bright fringe.

How is the distance between two second order maxima calculated?

The distance between two second order maxima can be calculated using the formula d = λL/d, where d is the distance between the slits, λ is the wavelength of the light, and L is the distance from the slits to the screen.

What factors can affect the distance between two second order maxima?

The distance between two second order maxima can be affected by the wavelength of the light, the distance between the slits, and the distance between the slits and the screen. It can also be affected by any obstructions or disturbances that may alter the interference pattern.

How does changing the distance between the slits affect the distance between two second order maxima?

Changing the distance between the slits will change the distance between two second order maxima. As the distance between the slits increases, the distance between two second order maxima will also increase. Similarly, as the distance between the slits decreases, the distance between two second order maxima will decrease.

What is the significance of the distance between two second order maxima?

The distance between two second order maxima is significant because it is a measure of the interference pattern created by the double-slit experiment. It can also be used to calculate the wavelength of the light being used, which is important in many scientific fields such as optics, spectroscopy, and astronomy.

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