Heated sodium has a strong yellow emission light at 595 nm. A diffraction gratin

Question

Heated sodium has a strong yellow emission light at 595 nm. A diffraction grating with an unknown line spacing is placed 50 cm in front of a screen. The grating is then illuminated with sodium light creating an interference pattern of bright yellow fringes on the screen. The first two bright fringes are measured to be 5.93 cm and 12.12 cm away from the central max.

a. Determine the distance between consecutive slits of the diffraction grating. To state this information in a more familiar way, also indicate how many lines per millimeter the diffraction grating contains.

b. How many total bright yellow fringes will be seen on the screen? Be sure to include the central max. and to account for the fringes both to the right and left of the center

Explanation / Answer

Part A)

Apply y/L = m(wavelength)/d

From the first to the central is 5.93

From the second to the central is 12.12, so between first and second its 12.12 - 5.93 = 6.19 cm

The average fo 5.93 and 6.17 = 5.995 cm to be used for the value of y

.05995/.5 = 1(595 X 10-9)/d

d = 4.96 X 10-6 m

For the lines per mm, 1/4.96 X 10-6 = 201513 lines per meter

divide by 1000 and get 201.5 lines per mm

Part B)
In this case 1 = m(595 X 10-9)/(4.96 X 10-6)

m = 8.34

We need a whole number value so that is 8

8 one each side plus the central is 17 fringes

Related Questions

Navigate

• Browse (All)
• Browse H
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.