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Answer:
a. i. 5.092 × 10²⁰ Hz ii. 588.98554 nm ii. 10667809.11 rad/m
b. i. 5.087 × 10²⁰ Hz ii. 589.58286 nm iii. 10657001.3 rad/m
Explanation:
refractive index, n = λ/λ' where λ = wavelength in vacuum = and λ' = wavelength in air
a. For λ = 589.15788 nm,
i. Frequency,
f = c/λ where c = speed of light in vacuum = 3 × 10⁸ m/s and λ = 589.15788 nm = 589.15788 × 10⁻⁹ m
So, f = 3 × 10⁸ m/s ÷ 589.15788 × 10⁻⁹ m
= 0.005092 × 10¹⁷ /s
= 5.092 × 10²⁰ /s
= 5.092 × 10²⁰ Hz
ii. Wavelength,
Since n = λ/λ' where λ = wavelength in vacuum = and λ' = wavelength in air
and n = 1.0002926
λ' = λ/n
= 589.15788 nm/1.0002926
= 588.98554 nm
k = 2π/λ'
= 2π/588.98554 nm
= 0.01066780911 rad/nm
= 0.01066780911 rad/nm × 10⁹ nm/1m
= 10667809.11 rad/m
b. For λ = 589.755 37 nm.,
i. Frequency,
f = c/λ where c = speed of light in vacuum = 3 × 10⁸ m/s and λ = 589.755 37 nm. = 589.755 37 × 10⁻⁹ m
So, f = 3 × 10⁸ m/s ÷ 589.755 37 × 10⁻⁹ m
= 0.005087 × 10¹⁷ /s
= 5.087 × 10²⁰ /s
= 5.087 × 10²⁰ Hz
ii. Wavelength,
Since n = λ/λ' where λ = wavelength in vacuum = and λ' = wavelength in air
and n = 1.0002926
λ' = λ/n
= 589.755 37 nm./1.0002926
= 589.58286 nm
k = 2π/λ'
= 2π/589.58286 nm
= 0.0106570013 rad/nm
= 0.0106570013 rad/nm × 10⁹ nm/1m
= 10657001.3 rad/m