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Chap_26_27_Disc[1] - 26-93 The focal length of a lens is...

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26-93: The focal length of a lens is inversely proportional to the quantity ( n ), 1 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 for red light and n n r 1572 . v 1605 . in violet light. Now, suppose a white object is placed 24.00 cm in front of a lens made from this type of glass. If the red light reflected from this object produces a sharp image 55.00 cm from the lens, where will the violet image be found? Picture the Problem : The figure shows an object 24.00 cm in front of a lens, for which the focal length is dependent on the wavelength of light. This results in different image distances for the red and violet light. Strategy: Calculate the focal length for the red light using equation 26-16 and the given data. Because the focal lengths are inversely proportional to ( n 1), use the ratio   v r r v 1 f f n n 1 to calculate the focal length for violet light. Finally, use equation 26-16 to calculate the image distance. Solution: 1. Calculate the focal length for red light: 1 1 r o i,r 1 1 1 1 16.709 cm 24.00 cm 55.00 cm f d d 2. Calculate the focal length of the violet light: r v r v 1 1.572 1 16.709 cm 15.80 cm 1 1.605 1 n f f n 3. Calculate the violet image distance: 1 1 i,v v o 1 1 1 1 46.2 cm 15.80 cm 24.00 cm d f d Insight: The violet light is in focus 8.8 cm before the red light. This blurring of the colors in an image is called chromatic aberration .
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