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B5. Consider an indoor wall picture captured by a small camera with a flash mounted on the camera. The illuminance produced by the flash, as a function of the object distance d, is Ev = (107 Im)/d². Assume that the object distance is much greater than the focal length, the flash is the only source of light, the object surface is Lambertian with the luminance of Ly = рЕy/n, where p = 18%. (a) Find an expression of the illuminance on the image detector in terms of the object distance d and the f-number (N) of the camera. (8 marks) [Hint: The image distance z' can be approximated as the focal length f.] (b) If the camera is an f/4 lens and the image detector requires a minimum illuminance of 10³ lm/m², find the maximum object distance that will produce a properly exposed image. (2 marks)