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.