A diffraction grating has 600 lines/mm. Light with a wavelenght of 600nm is incident on it. A screen is placed 0.1m from the grating. Calculate the distance from the 1st and 2nd order maxima on the screen

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To calculate the distance from the first and second order maxima on the screen, we need to use the equation for the angular position of the maxima in a diffraction grating:

λ = d * sin(θ)

where λ is the wavelength of light, d is the line spacing of the grating, and θ is the angle between the incident light and the diffracted light.

First, we need to convert the line spacing (d) from lines per millimeter (lines/mm) to meters (m). We can use the following conversion factor:

1 mm = 0.001 m

So, for a grating with 600 lines/mm, the line spacing (d) is:

d = 1 / 600 mm = 0.00167 m

Next, we can calculate the angle θ for the first order maximum (m = 1):

θ1 = sin^(-1)(λ / d)

θ1 = sin^(-1)(600 nm / 0.00167 m)

Calculating this using a scientific calculator or software, the value of θ1 comes out to be approximately 20.25 degrees.

Now, to find the distance from the first order maximum on the screen, we can use some trigonometry. The distance (L) can be calculated from the following equation:

L = x * tan(θ1)

where x is the distance from the grating to the screen.

Given that the screen is placed 0.1 m from the grating, we can substitute this value into the equation:

L = 0.1 m * tan(20.25 degrees)

Calculating this, the value of L comes out to be approximately 0.036 m or 36 mm.

For the second order maximum (m = 2), we can use the same calculations, but with θ2:

θ2 = sin^(-1)(2 * λ / d)

θ2 = sin^(-1)(2 * 600 nm / 0.00167 m)

Calculating this, the value of θ2 comes out to be approximately 43.75 degrees.

Now, using the same equation as before, we can find the distance from the second order maximum on the screen:

L = 0.1 m * tan(43.75 degrees)

Calculating this, the value of L comes out to be approximately 0.150 m or 150 mm.

Therefore, the distance from the first order maximum on the screen is approximately 36 mm, and the distance from the second order maximum is approximately 150 mm.