1. You are given a slide with two slits cut into it and asked how far apart the

Question

1. You are given a slide with two slits cut into it and asked how far apart the slits are. You shine white light on the slide and notice the first-order color spectrum that is created on a screen 3.75 m away. On the screen, the red light with a wavelength of 714 nm is separated from the violet light with a wavelength of 404 nm by 8.00 mm. What is the separation of the two slits?

_____ mm

2. A grating has 3040.1 slits per cm. How many orders of light of wavelength 438 nm can be observed with this grating?

______

Explanation / Answer

we can use this equation because the angles are small enough that sin theta is so nearly equal to tan theta.

x = n L lambda / d
x is distance of image from central point on screen
n = order of image (1 in this case)
lambda = wavelength (we'll convert them to meters)
d = distance between slits (it will come out in meters)

we do not know the actual values of x but we do know the difference between them for the two given wavelengths.
so
7.50E-3 = Xr - Xv = (1 (3.60) (689E-9) / d ) - ( 1 (3.60) (392E-9) / d )
7.50E-3 = 1.069E-6 / d
d = 1.426E-4 m or 0.1426 mm (0.143 mm to 3 s.f.)

Related Questions

Navigate

• Browse (All)
• Browse 1
• Subjects

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