Question

You notice a person is wearing a violet shirt. Answer the following questions.

A) What is the frequency of the light your eyes are observing assuming the prominent wavelength you are observing is 400 nm?

B) What is the frequency range of the light being absorbed by the clothing material?

C) What is the color associated with the light absorbed by the clothing?

D) If the intensity of light absorbed by the clothing is 1,399 lumens, and the light observed by your eye is 944 lumens, what is the absorbance of the shirt?

D) What is the %T of part d?

Answer 1

A.

Wave length = 400 nm .
nm means nanometer and 1 nm is equal to 1 x 10^-9 m
So, 400 nm = 400 x 10^-9 m = 4.0 x 10^-7 m

Speed of light, c is 3 x 10⁸ m/s

frequency = c / wavelength
= (3 x 10⁸ m/s) / (4.0 x 10^-7 m)
= 7.5 x 10¹⁴ s^-1
= 7.5 x 10¹⁴ hertz

B.

The violet light has a wavelength of about 400 nm.

1 nm is equal to 1 x 10^-9 m

So, 400 nm = 400 x 10^-9 m = 4.0 x 10^-7 m

Speed of light, c is 3 x 10⁸ m/s

frequency = c / wavelength
  = (3 x 10⁸ m/s) / (4.0 x 10^-7 m)
= 7.5 x 10¹⁴ s^-1
= 7.5 x 10¹⁴ hertz

C.

Violet = red + Blue

Absorbed = all colours except red and blue

Reflected = red and blue

Just remember that the three primary colours of light are Red, Blue and Green

The colour of the object is the combination of the colours it reflect

Yellow = Green and Red
Violet/Magenta = Red and Blue
Cyan=Green and Blue

D.

I₀ = initial light intensity = 1,399 lumens

I = light intensity after it passes through = 944 lumens

A = - log T
= - log (I / I_o)
​ = - log (944 / 1399)
​ = - log (0.675)
​ = 0.17

E.

Transmittance,T = I / I_o

% Transmittance, %T = 100 T
= 100(944 / 1399)
= 67.48 %