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attashe74 [19]
3 years ago
12

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 th

e 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?
Physics
1 answer:
Ainat [17]3 years ago
5 0

Answer:

46.22 cm

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} = \frac{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

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