The focal length of a lens is inversely proportional to the quantity ( n 1), whe
ID: 1618903 • Letter: T
Question
The focal length of a lens is inversely proportional to the quantity (n1), where n is the index of refraction of the lens 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 of nr= 1.570 for red light and nv= 1.598 in violet light. Now, suppose a white object is placed 21.50 cm in front of a lens made from this type of glass.
If the red light reflected from this object produces a sharp image 55.00 cm from the lens, where will the violet image be found?
di,viol=______ cmExplanation / Answer
As the focal length is inversly proportional to (n-1) => f 1/(n-1) eqn (1)
Image formation due to red light, 1/v-1/u = 1/f
=> 1/f = 1/v-1/u =1/55-1/21.5
=>fred=-35.30 cm
From proportionality relation eqn (1),
fred/ fviolet = (nviolet-1)/(nred-1) = 0.598/0.570 =1.049
=> fviolet = fred/1.05 = -35.30/1.049 = -33.65cm
Now for the location of image for violet light
1/v-1/u = 1/ f=> 1/v = 1/u+1/f = 1/21.50 -1/33.65
=>v = 59.54cm
The image due to the violet light is formed at 59.54 cm from the lens.