91Ó°ÊÓ

Light incident on a pair of slits produces an interference pattern on a screen \(2.50 \mathrm{m}\) from the slits. If the slit separation is $0.0150 \mathrm{cm}$ and the distance between adjacent bright fringes in the pattern is \(0.760 \mathrm{cm},\) what is the wavelength of the light? [Hint: Is the small-angle approximation justified?]

Ramon has a coherent light source with wavelength \(547 \mathrm{nm} .\) He wishes to send light through a double slit with slit separation of $1.50 \mathrm{mm}\( to a screen \)90.0 \mathrm{cm}$ away. What is the minimum width of the screen if Ramon wants to display five interference maxima?

Light from a helium-neon laser \((630 \mathrm{nm})\) is incident on a pair of slits. In the interference pattern on a screen \(1.5 \mathrm{m}\) from the slits, the bright fringes are separated by \(1.35 \mathrm{cm} .\) What is the slit separation? [Hint: Is the small angle approximation justified?]

Light of wavelength 589 nm incident on a pair of slits produces an interference pattern on a distant screen in which the separation between adjacent bright fringes at the center of the pattern is \(0.530 \mathrm{cm} .\) A second light source, when incident on the same pair of slits, produces an interference pattern on the same screen with a separation of $0.640 \mathrm{cm}$ between adjacent bright fringes at the center of the pattern. What is the wavelength of the second source? [Hint: Is the small-angle approximation justified?]

A double slit is illuminated with monochromatic light of wavelength $600.0 \mathrm{nm} .\( The \)m=0\( and \)m=1\( bright fringes are separated by \)3.0 \mathrm{mm}\( on a screen \)40.0 \mathrm{cm}$ away from the slits. What is the separation between the slits? [Hint: Is the small angle approximation justified?]

Gratings A grating has exactly 8000 slits uniformly spaced over \(2.54 \mathrm{cm}\) and is illuminated by light from a mercury vapor discharge lamp. What is the expected angle for the third-order maximum of the green line $(\lambda=546 \mathrm{nm}) ?$

A red line (wavelength \(630 \mathrm{nm}\) ) in the third order overlaps with a blue line in the fourth order for a particular grating. What is the wavelength of the blue line?

Red light of 650 nm can be seen in three orders in a particular grating. About how many slits per centimeter does this grating have?

A grating has 5000.0 slits/cm. How many orders of violet light of wavelength \(412 \mathrm{nm}\) can be observed with this grating? (tutorial: grating).

A grating is made of exactly 8000 slits; the slit spacing is $1.50 \mu \mathrm{m} .\( Light of wavelength \)0.600 \mu \mathrm{m}$ is incident normally on the grating. (a) How many maxima are seen in the pattern on the screen? (b) Sketch the pattern that would appear on a screen \(3.0 \mathrm{m}\) from the grating. Label distances from the central maximum to the other maxima.