The focal length of a lens is inversely proportional to the quantity (n-1), where n is the index of refraction of the lens of the material. the value of n, however, depends on the wavelength of the light that passes through the lens. for example, one type of flint glass has an index of refraction if n=1.572 for red light and n=1.605 in violet light. now suppose a white object is placed 24.00cm in front of a lens made from this type of glass. if the red light reflected from this object produces a sharp image 55.00cm from the lens , where will the violet image be found?

46.22 cm

Explanation:

The focal refraction, fr is given by

The focal red light is given by

and making fr the subject we obtain

fv = 0.945455* 16.70886 cm = 15.79747 cm

Therefore, violet image is approximately 46.22 cm

a and b sometimes have a positive value

scattering of light by tiny particles in air to produce the colors we see on sky, is dependent on the following factors:

(i) wavelength of light

(ii) size of the scattering particle  

(iii) distance traveled by light through the atmosphere.

according to rayleigh's law of scattering, the amount of scattering is inversely proportional to the fourth power of its wavelength. shorter the wavelength, greater is its scattering. hence violet/blue light is scattered more than red.

sun's light is a composite light ( visible light) with wavelengths in the range 400 nm (violet) to 700 nm (red). as sunlight passes through our atmosphere, the molecules of air scatter light according to their wavelengths. during sunrise and sunset, the sun's position is below the horizon. hence light from the sun travels a greater distance in the atmosphere when compared to its position a noon.

as sunlight enters the earth's atmosphere, blue light is scattered away and at the end of its journey in the sky, only red and orange wavelengths remain in the beam.

hence at sunrise and sunset, the sky appears reddish orange.