The focal length of a lens is inversely proportional to the quantity (n - 1), wh
ID: 1619779 • Letter: T
Question
The focal length of a lens is inversely proportional to the quantity (n - 1), where n is the index of retraction 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 n_x = 1.560 for red light and n_r = 1, 608 in violet light. Now, suppose a white object is placed 25.50cm in front of a lens made from this type of glass. Part A If the red light reflected from this object produces a sharp image 58.00 cm from the lends, where will the violet image be found?Explanation / Answer
Answer:
Step 1: Need to calculate focal length for red light: Focal length for red light (fr) = (1/do+1/dir)-1
where, do= distance of object; dir= distance of image from lens due to reflection of red light
(fr) = (1/25.50 + 1/58)-1
fr= 17.71 cm
Step 2: Claculate the focal length for violet light: fv = fr(nr-1/nv-1)
where nr and nv are the refractive indef for the red and violet, respectively.
fv = 17.713 * (1.560-1 / 1.608-1)
fv = 16.315 cm
Step 3: calculate the distance of violet image:
div = (1/fv - 1/do)-1
where, div= distance of violet image;
div = (1/16.315 - 1/25.50)-1
div = 45.66 cm.