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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

A diffraction grating is made up of silts of width 300 nm with separation 900 nm. The grating is illuminated by monochromatic plane waves of wavelength位=600鈥�nm at normal incidence. (a) How many maxima are there in the full diffraction pattern? (b) What is the angular width of a spectral line observed in the first order if the grating has 1000 slits?

Aslit 1.00mmwide is illuminated by light of wavelength 589nm. We see a diffraction pattern on a screen 3.00maway. What is the distance between the first two diffraction minima on the same side of the central diffraction maximum?

How far from grains of red sand must you be to position yourself just at the limit of resolving the grains if your pupil diameter is 1.5mm, the grains are spherical with radius50渭m , and the light from the grains has wavelength 650nm? (a) If the grains were blue and the light from them had wavelength 400nm, would the answer to (b) be larger or smaller?

(a) Show that the values of a at which intensity maxima for single-slit diffraction occur can be found exactly by differentiating Eq. 36-5 with respect to a and equating the result to zero, obtaining the condition tan伪=伪. To find values of a satisfying this relation, plot the curve y=迟补苍伪 and the straight line y=伪 and then find their intersections, or use 伪calculator to find an appropriate value of a by trial and error. Next, from 伪=(m+12)蟺, determine the values of m associated with the maxima in the singleslit pattern. (These m values are not integers because secondary maxima do not lie exactly halfway between minima.) What are the (b) smallest and (c) associated , (d) the second smallest 伪(e) and associated , (f) and the third smallest (g) and associated ?

A diffraction grating has 200 lines/mm. Light consisting of a continuous range of wavelengths between 550 nm and 700 nm s incident perpendicularly on the grating.

(a) What is the lowest order that is overlapped by another order?

(b) What is the highest order for which the complete spectrum is present?
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