Question

For a grating, how many lines per millimeter would be required for the first order diffraction line for λ = 400 nm to be observed at a reflection angle of 5o when the angle of incidence is 45o?

Answer 1

Answer:

For a grating, how many lines per millimeter would be required for the first order diffraction line for λ = 400 nm to be observed at a reflection angle of $5^{o}$ when the angle of incidence is  $45^{o}$?

The number of lines per mm is 1985 lines

Explanation:

A diffraction grating is used to separate a light source with multiple wavelengths into single wavelengths of different colors using the principle of diffraction.

Calculating for the spacing between the reflected surfaces

The spacing between the reflecting surfaces can be obtained using the relationship with the wavelength as shown below;

nA = d (sin i + sin r) ....................................1

where n is the order of diffraction = 1;

A is the wavelength = 400 nm

i is the angle of incidence = $45^{o}$

r is the angle of refraction =  $5^{o}$

making d the subject formula from equation 1 we have;

$d = \frac{nA}{sin i + sin r}$...........................2

Now we substitute the given parameters into equation 2;

$d = \frac{1(400 nm)}{(sin 45^{o} ) + (sin 5^{o} )}$

d = $\frac{400 nm}{0.707 +0.087}$

d = 503.7 nm

The spacing between reflecting surfaces is 503.7 nm

Calculating for the number of lines per millimeter

To calculate the number of spacing per millimeter we convert nanometer to millimeters, 1 mm =$10^{6}$ and 1 line = 503.7 nm;

$1 mm *\frac{1 line}{503.7 nm} *\frac{10^{6} }{mm}$

= 1985 lines

Therefore the number of lines per millimeter would be 1985 lines