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Chapter 36: Q106P (page 1115)

Light of wavelength 500nm diffracts through a slit of width2渭m and onto a screen that is 2maway. On the screen, what is the distance between the center of the diffraction pattern and the third diffraction minimum?

Short Answer

Expert verified

The distance between the center of the diffraction pattern and the third diffraction minimum is1.5mm .

Step by step solution

01

Given data:

The wavelength of incident light 位=500nm:

Slit width: d=2mm

Distance of screen from slit: D=2m

02

Diffraction from a single slit:

The distance of the mth order single slit diffraction minima from thecentral maxima for slit width d and screen distance D is

x=m位Dd .....(1)

Here,位 is the wavelength of the incident light.

03

Determining the distance of the third minimal from central maxima

Calculate the distance of the third minima from the central maxima by substituting known values into equation (1).

x=3脳500脳10-9m脳2m2脳10-3m=0.0015m=1.5mm

Thus, the required distance is 1.5mm.

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Most popular questions from this chapter

Light of wavelength 440 nm passes through a double slit, yielding a diffraction pattern whose graph of intensity I versus angular position is shown in Fig. 36-44. Calculate (a) the slit width and (b) the slit separation. (c) Verify the displayed intensities of the m=1and m=2 interference fringes.

A spy satellite orbiting at 160 km above Earth鈥檚 surface has a lens with a focal length of 3.6 m and can resolve objects on the ground as small as 30 cm. For example, it can easily measure the size of an aircraft鈥檚 air intake port. What is the effective diameter of the lens as determined by diffraction consideration alone? Assume 位=550nm.

A diffraction grating illuminated by monochromatic light normal to the grating produces a certain line at angle . (a) What is the product of that line鈥檚 half-width and the grating鈥檚 resolving power? (b) Evaluate that product for the first order of a grating of slit separation 900 nm in light of wavelength 600 nm.

With a particular grating the sodium doublet (589.00 nm and 589.59 nm) is viewed in the third order at 10掳 to the normal and is barely resolved. Find (a) the grating spacing and (b) the total width of the rulings.

Figure shows a red line and a green line of the same order in the pattern produced by a diffraction grating. If we increased the number of rulings in the grating 鈥� say, by removing tape that had covered the outer half of the rulings 鈥� would (a) the half-widhts of the lines and (b) the separation of the lines increase, decrease, or remain the same? (c) Would the lines shift to the right, shift to the left, or remain in place
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