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In solving the problem of increasing the power of lenses to ignite fires, M.V. Lomonosov constructed the instrument shown in Fig. and called it the catoptric-dioptic igniting instrument. Here A1, A2, A3, A5 are plane mirrors and B1, B2, B2, B4, B5 are converging lenses. Determine the angle at which the mirrors should be set and the smallest dimensions of these mirrors to ensure that the amount of light passing through each lens is the same. The lens diameter is d. Assume the mirrors B1, B2, B3 and B5 to be symmetrically placed on the corners of a square.

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The perpendiculars to mirrors A1 and A2 should make an angle of 22°30' to the incident rays; the perpendiculars to mirrors A3 and A5 , 67°30'. The size of all the mirrors should not be less than the diameter d of the lenses: the width of mirrors A1 and A2 should be equal to d/cos(22°30') ≅ 1.08d and the width of mirrors A1 and A2 should be equal to 2.61 d.  

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