What Is the Correct Spacing for Diffraction Grating Lines?

[tambourine]

Homework Statement

A diffraction grating produces a third-order maximum, at an angle of 22 degrees, for red light (694.3 nm). Determine the spacing of the lines.

Homework Equations

for maxima:

sin θm = mλ/d

where m is the order of the maxima, λ is the wavelength in nm, and d is the spacing of the lines

The Attempt at a Solution

λ = 694.3 nm
θ = 22
m = 3

d = mλ / sin θ
d = 3 (694.3) / sin 22
d = 5560 nm

but the answer in the textbook is 7400 nm. what have i done wrong?

and this one:

Calculate the highest spectral order visible when a 6200-line/cm grating is illuminated with 633-nm laser light.

d = 1/6200 cm
λ = 633 nm = 6.33 x 10^9 cm
n = ?

how do i find n without θ? I'm probably missing some obvious things

 

[tambourine]

interference in thin films:

A transparent oil (n=1.29) spills onto the surface of water (n=1.33), producing a maximum of reflection with normally incident orange light, with a wavelength of 6.00 x 10^-7 m in air. Assuming the maximum occurs in the first order, determine the thickness of the oil slick.

n[oil] = λair/λoil

where n is the index of refraction of oil

λoil = n[oil]λair
= 1.29(6.00 x 10^-7)
λoil = 7.74 x 10^-7

then,

t = λoil / 4

where t is the thickness of the oil and λ/4 is when the first maximum occurs

t = 7.74 x 10^-7/4
t = 1.935 x 10^-7 m = 193.5 nm

the answer is supposed to be 233 nm.

 

[baba89]

here, but could you provide some guidance on how to approach these problems?



It looks like you have the correct equations and approach for both problems. For the first problem, make sure that you are using the correct units for the spacing of the lines. The answer in the textbook is given in nanometers (nm), so you may need to convert your answer from centimeters (cm) to nanometers. Additionally, double check your calculations to make sure there are no errors.

For the second problem, you are correct that you cannot find the order (n) without knowing the angle (θ). This is because the equation for maxima involves both the order and the angle. It is possible that this problem is asking for the maximum order that can be seen with the given grating, in which case you would use the equation n = d/λ. This would give you the order in terms of the spacing of the lines and the wavelength, rather than the angle. However, without more information, it is difficult to determine the correct approach for this problem. I would recommend checking with your teacher or referring to the textbook for clarification.