91Ó°ÊÓ

A single slit of width \(0.140 \mathrm{~mm}\) is illuminated by monochromatic light, and diffraction bands are observed on a screen \(2.00 \mathrm{~m}\) away. If the second dark band is \(16.0 \mathrm{~mm}\) from the central bright band, what is the wavelength of the light?

Green light of wavelength \(500 \mathrm{~nm}\) is incident normally on a grating. and the second-order image is diffracted \(32.0^{\circ}\) from the normal. How many lines \(/ \mathrm{cm}\) are marked on the grating?

A narrow beam of yellow light of wavelength \(600 \mathrm{~nm}\) is incident normally on a diffraction grating ruled 2000 lines \(/ \mathrm{cm}\), and images are formed on a screen parallel to the grating and \(1.00 \mathrm{~m}\) distant. Compute the distance along the screen from the central bright line to the first-order lines.

Blue light of wavelength \(4.7 \times 10^{-7} \mathrm{~m}\) is diffracted by a grating ruled 5000 lines \(/ \mathrm{cm} .(a)\) Compute the angular deviation of the second-order image. ( \(b\) ) What is the highest-order image theoretically possible with this wavelength and grating?

Determine the ratio of the wavelengths of two spectral lines if the second- order image of one line coincides with the third-order image of the other line, both lines being examined by means of the same grating.

A spectrum of white light is obtained with a grating ruled with 2500 lines \(/ \mathrm{cm}\). Compute the angular separation between the violet \(\left(\lambda_{v}=400 \mathrm{~nm}\right)\) and \(\operatorname{red}\left(\lambda_{r}=700 \mathrm{~nm}\right)\) in the \((a)\) first order and \((b)\) second order. (c) Does yellow \(\left(\lambda_{y}=600 \mathrm{~nm}\right.\) ) in the third order overlap the violet in the fourth order?

How far apart are the diffracting planes in a \(\mathrm{NaCl}\) crystal for which X-rays of wavelength \(1.54 \AA\) make a glancing angle of \(15^{\circ} 54^{\prime}\) in the first order