Question

Calculate the wavelength of light that has its second-order maximum at 45.0º when falling on a diffraction grating that has 5000 lines per centimeter.

a) 450 nm
b) 500 nm
c) 550 nm
d) 600 nm

Answer 1

To calculate the wavelength of light that has its second-order maximum at 45.0° when falling on a diffraction grating, we can use the equation sinθ = mλ/d. Given that the grating has 5000 lines per centimeter, the spacing between the lines is 1/5000 cm. By substituting the values into the equation, we find that the wavelength of light is 450 nm.

Step-by-step explanation:

To calculate the wavelength of light that has its second-order maximum at 45.0° when falling on a diffraction grating, we can use the equation for diffraction grating:

sinθ = mλ/d

Where:

• θ is the angle of the maximum
• m is the order of the maximum, in this case, 2
• λ is the wavelength of light
• d is the spacing between the lines on the grating

Given that the grating has 5000 lines per centimeter, we can calculate the spacing between the lines:

d = 1/5000 cm

Substituting the values into the equation:

sin(45.0°) = 2λ/(1/5000)

λ = (1/5000) / sin(45.0°) = 450 nm

Therefore, the wavelength of light is 450 nm.