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Chapter 33: Q. 3 (page 955)

A double-slit experiment is performed with light of wavelength $630 nm$ . The bright interference fringes are spaced $1.8 mm$ apart on the viewing screen. What will the fringe spacing be if the light is changed to a wavelength of $420 nm$ $?$

Short Answer

Expert verified

Due to light changes fringe spacing is $1.2 mm$ .

Step by step solution

01

Formula for position of bright fringes

In the double slit experiment, the position of the bright fringes can be written as follows:

$y_{m} = \frac{尘位尝}{d}$

As a result, the distance between any two consecutive brilliant fringes is

$螖测 = y_{m + 1} - y_{m} = \frac{(m + 1) 位尝}{d} - \frac{尘位尝}{d} = \frac{位尝}{d}$

02

Calculation for fringe space

This equation can be rearranged to find the ratio $(L / d)$ .

$\frac{L}{d} = \frac{螖测}{位}$

$= \frac{1.8 脳 10^{- 3} m}{630 脳 10^{- 9} m}$

$= 2857$

This constant ratio can now be used to calculate the fringe spacing for a wavelength of $420 nm$ .

$螖测 = \frac{位尝}{d} = 420 脳 10^{- 9} m 脳 2857$

$螖测 = 1.2 mm$

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Most popular questions from this chapter

3. FIGURE Q33.3 shows the viewing screen in a double-slit experiment. Fringe $C$ is the central maximum. What will happen to the fringe spacing if

a. The wavelength of the light is decreased?

b. The spacing between the slits is decreased?

c. The distance to the screen is decreased?

d. Suppose the wavelength of the light islocalid="1649170567955" $500 nm$ . How much farther is it from the dot on the screen in the center of fringe E to the left slit than it is from the dot to the right slit?

FIGURE $P 33.56$ shows the light intensity on a screen behind a single slit. The wavelength of the light is $600 nm$ and the slit width is $0.15 mm$ . What is the distance from the slit to the screen?

Scientists use laser range-finding to measure the distance to the moon with great accuracy. A brief laser pulse is fired at the moon, then the time interval is measured until the "echo" is seen by a telescope. A laser beam spreads out as it travels because it diffracts through a circular exit as it leaves the laser. In order for the reflected light to be bright enough to detect, the laser spot on the moon must be no more than $1.0 km$ in diameter. Staying within this diameter is accomplished by using a special large diameter laser. If $位 = 532 nm$ , what is the minimum diameter of the circular opening from which the laser beam emerges? The earth-moon distance is $384, 000 km .$

In a single-slit experiment, the slit width is $200$ times the wavelength of the light. What is the width $(in mm)$ of the central maximum on a screen $2.0 m$ behind the slit $?$

FIGURE shows the light intensity on a viewing screen behind a single slit of width $a$ . The light鈥檚 wavelength is $位$ . Is $位 < a$ , $位 = a$ , $位 > a$ , oris it not possible to tell? Explain.

See all solutions

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