(b) What is the name and the function of the pa labelled C? [2] (c) Suppose constructive interference of light witl wavelength \( \lambda \) is occurring at the centre of the detector iimum distance that mirror \( M_{1} \) can be shifted so that the interference changes to return erference in a different position? \( [1] \) bands will shift past a fixed point on the detector if the wavelength of the light is \( 660 \mathrm{~nm} \) \( M_{1} \) is moved \( 0.100 \mathrm{~mm} \) towards the compensating plate? [2] (Chapter 16): A laser beam \( (\lambda=630 \mathrm{~nm}) \) goes through a double slit with separation terference pattern is projected on a screen \( 5 \mathrm{~m} \) away, what is the distance between the thir ge and the central bright fringe? \( [4 \) (Chapter 17): A diffraction grating has 2500 lines uniformly spaced over \( 10 \mathrm{~mm} \). It pendicularly with the yellow light of a sodium lamp, which contains two wavelength \( \mathrm{Im} \) and \( 589.59 \mathrm{~nm} \) (the sodium doublet). (a) At what angles will the second order maxim velengths occur? Hence obtain their separation. (b) Suppose the interference pattern screen \( 1 \mathrm{~m} \) away: how far apart would the two peaks be? hapter 18): Monochromatic light with wavelength \( 538 \mathrm{~nm} \) is incident on a single slit w
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Two slits of width $2 \mu \mathrm{m},$ each in an opaque material, are separated by a center-to-center distance of $6 \mu \mathrm{m}$. A monochromatic light of wavelength $450 \mathrm{nm}$ is incident on the double-slit. One finds a combined interference and diffraction pattern on the screen. (a) How many peaks of the interference will be observed in the central maximum of the diffraction pattem? (b) How many peaks of the interference will be observed if the slit width is doubled while keeping the distance between the slits same? (c) How many peaks of interference will be observed if the slits are separated by twice the distance, that is, $12 \mu \mathrm{m}$, while keeping the widths of the slits same? (d) What will happen in (a) if instead of 450-nm light another light of wavelength $680 \mathrm{nm}$ is used? (e) What is the value of the ratio of the intensity of the central peak to the intensity of the next bright peak in (a)? (f) Does this ratio depend on the wavelength of the light? (g) Does this ratio depend on the width or separation of the slits?
Coherent light of wavelength 501.5 nm is sent through two parallel slits in an opaque material. Each slit is 0.700$\mu \mathrm{m}$ wide. Their centers are 2.80$\mu \mathrm{m}$ apart. The light then falls on a semi cylindrical screen, with its axis at the mid line between the slits. We would like to describe the appearance of the pattern of light visible on the screen. (a) Find the direction for each two-slit interference maximum on the screen as an angle away from the bisector of the line joining the slits. (b) How many angles are there that represent two-slit interference maxima? (c) Find the direction for each single-slit interference minimum on the screen as an angle away from the bisector of the line joining the slits. (d) How many angles are there that represent single-slit interference minima? (e) How many of the angles in part (d) are identical to those in part (a)? (f) How many bright fringes are visible on the screen? (g) If the intensity of the central fringe is $I_{\max },$ what is the intensity of the last fringe visible on the screen?
FIGURE CP22.74 shows light of wavelength $\lambda$ incident at angle $\phi$ on a reflection grating of spacing $d$. We want to find the angles $\theta_{m}$ at which constructive interference occurs. a. The figure shows paths 1 and 2 along which two waves travel and interfere. Find an expression for the path-length difference $\Delta r=r_{2}-r_{1}$ b. Using your result from part a, find an equation (analogous to Equation 22.15 ) for the angles $\theta_{m}$ at which diffraction occurs when the light is incident at angle $\phi .$ Notice that $m$ can be a negative integer in your expression, indicating that path 2 is shorter than path $1 .$ c. Show that the zeroth-order diffraction is simply a "reflection." That is, $\theta_{0}=\phi$ d. Light of wavelength 500 nm is incident at $\phi=40^{\circ}$ on a reflection grating having 700 reflection lines/mm. Find all angles $\theta_{m}$ at which light is diffracted. Negative values of $\theta_{m}$ are interpreted as an angle left of the vertical. e. Draw a picture showing a single 500 nm light ray incident at $\phi=40^{\circ}$ and showing all the diffracted waves at the correct angles. (FIGURE CAN'T COPY)
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