Question

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?

Answer 1

46.22 cm

Step-by-step explanation:

The focal refraction, fr is given by

`fr = \frac {c}{(1.572 -1)}  = \frac {c}{0 .572}`

The focal red light is given by

`fv = \frac {c}{(1.605 - 1)} = \frac {c}{0.605}`

`\frac {fv}{fr} = \frac {0.572}{0 .605} = 0.945455`

`\frac {1}{fr} = (1)/(image) + \frac {1}{object}` and making fr the subject we obtain

`fr = \frac {image * object}{(image + object)} = \frac {24.00 * 55} {(24.0 + 55)} = 16.70886 cm`

fv = 0.945455* 16.70886 cm = 15.79747 cm

`image = \frac {object * f} {(object - f)} = \frac {15.79747 * 24.0}{(24.0 - 15.79747)} = 46.22222 cm`

Therefore, violet image is approximately 46.22 cm