Explanation Given info: The object distance is 24 cm , the refractive index of red light is 1.572 , the refractive index of violet light is 1.605 and image distance of red light is 55.00 cm The focal length is inversely proportional to the term ( n − 1 ) f ∝ 1 n − 1 Here, n is the refractive index. The formula to calculate the focal length of red light is, f r = 1 n r − 1 Here, n r is the refractive index of red light. The formula to calculate the focal length of red light is, 1 f r = 1 v r − 1 u Here, u is the object distance. v r is the image distance of red light. Substitute 1 n r − 1 for f r in the above formula. 1 f r = 1 v r − 1 u 1 n r − 1 = 1 v r − 1 u (1) The formula to calculate the focal length of violet light is, f v = 1 n v − 1 Here, n v is the refractive index of violet light. The formula to calculate the focal length of violet light is, 1 f v = 1 v v − 1 u Here, u is the object distance. v v is the image distance of violet light. Substitute 1 n v − 1 for f v in the above formula. 1 f v = 1 v v − 1 u 1 n v − 1 = 1 v v − 1 u (2) Divide equation (1) and (2)

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Chapter 26, Problem 86PCE

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The image distance of violet light.

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Chapter 26, Problem 85PCE

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The image distance of violet light.

Solution Summary: The author explains that the image distance of violet light is 47.3cm. The focal length is inversely proportional to the term (n-1).

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The image distance of violet light.

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