How would you solve this problem with and without the small angle approximation?

Question

How would you solve this problem with and without the small angle approximation? I would like to compare my answers with someone else's. I can't figure out how to solve the problem without the small approximation. Any help is much appreciated.

17. A lab technician uses laser light with a wavelength of 670 nm to test a diffraction grating. When the grating is 40.0 cm from the screen, the first-order maxima appear 6.00 cm from the center of the pattern. How many lines per millimeter does this grating have

Explanation / Answer

here,

wavelength, w = 670 nm = 9.70*10^-7 m

distance to screen, D = 40 cm = 0.4 m

screen width, Y = 6 cm = 0.06 m

order of diffraction, m = 1

from diffraction experiment:

Y = m*w*D/d

slit width, d = m*w*D/Y

slit width, d = 1 * 9.70*10^-7 * 0.4/0.06

slit width, d = 6.467*10^-6 m

slit width, d = 4.467*10^-3 mm

lines per mm, n = 1/d

lines per mm, n = 1/(4.467*10^-3)

lines per mm, n = 223.864 or 224 /mm

Related Questions

Navigate

• Browse (All)
• Browse H
• Subjects

---

---

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