Question

laser light sent through a double slit produces an interference pattern on a screen 3.0 m from the slits. If the eighth order maximum occurs at an angle of 12.0, at what angle does the third order maximum occur

Answer 1

The third order maximum will occur at a smaller angle than the eighth order maximum, and will have an angle proportional to the ratio of their order numbers. Without the actual wavelength and slit separation, the exact angle cannot be calculated, but it will be less than 12.0 degrees.

Step-by-step explanation:

The student is asking about the phenomenon of interference patterns as observed in Young's Double Slit Experiment in optics. To find at what angle the third order maximum occurs, we can use the formula for the angular position of the maxima in interference patterns:

mλ = d sin(θ)

Where m is the order of the maximum, λ is the wavelength of the light, d is the slit separation, and θ is the angle of the maximum from the central axis.

To solve for the angle at which the third order maximum occurs without knowing the actual wavelength or slit separation, we need to understand that the angle is directly proportional to the order of the maximum. If the eighth order maximum occurs at 12.0 degrees, it's reasonable to assume that the third order will occur at a smaller angle, proportional to the ratio of the orders (3/8). Since we don't have the actual wavelength(λ) and slit separation(d), we can't calculate the exact angle for the third order maximum. However, the relationship between the angles of the different order maxima will be consistent with the ratios of their order numbers. Therefore, you can expect the angle for the third order maximum to be less than 12.0 degrees.

Answer 2

Given the laser light which is sent through the double slit produces an interference pattern on the screen placed 3 meters from the slits.

The 8th order maximum occurs at angle = 12

So,

`$8^(th) \text{ order maxima} = d \sin \theta = m \lambda$` , m = 8

`$d = (8 \lambda)/(\sin 12)$`

`$(\lambda)/(d)= (\sin 12)/(8)$`

`$3^(rd) \text{ order maxima}= d \sin \theta_2 = m_2 \lambda$`

`$\sin \theta_2 = (m_2 \lambda)/(d)=(3 \lambda)/(d)$`
`$=0.75\ {\sin 12}$`

`$\theta_2 = \sin^(-1)\left(0.75\ \sin 12\right)$`

`$ = \sin^(-1)\left(0.155)$`

`$=8.91^\circ$`