The focal length of a lens is inversely proportional to the quantity (n1), where
ID: 1570948 • 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= 1.572 for red light and nv= 1.597 in violet light. Now, suppose a white object is placed 27.00 cm in front of a lens made from this type of glass.
If the red light reflected from this object produces a sharp image 55.50 cm from the lens, where will the violet image be found? di,viol= ______________cm
Explanation / Answer
Solution:
Since the image distance is 55.5 cm and objectdistance is 27 cm , the magnification m = -55.5/27 = -2.1
This shows the type of lens is a converging (positive lens)
if fr= focal length for red , 1/f = 1/do + 1/di
=> 1/ fr = 1/27 + 1/55.5 = 0.55 => focal length = f = 1/0.055 = 18.2 cm
nr = 1.572 , nv = 1.597
focal length for violet = fr [(nr-1)/(nv-1)] = (18.2) [ (1.572 -1) / (1.597-1) ] = 17.4 cm
1/fv = 1/do + 1/div =>
image distance for violet = div = [ 1/fv - 1/do ]-1 = [ 1/17.4 - 1/27 ]-1 = 49 cm