Question

Light containing two different wavelengths passes through a diffraction grating with 1300 slits/cm. On a screen 16.0 cm from the grating, the third-order maximum of the shorter wavelength falls midway between the central maximum and the first side maximum for the longer wavelength. If the neighboring maxima of the longer wavelength are 8.44 mm apart on the screen, what are the wavelengths in the light? (Hint: Use the small angle approximation.)

Answer 1

1/130000 * sinTheta=1*lambda

but sinTheta=tantheta=8.44/160

now solve for lambda, in m