Two identical concave mirrors of focal length f face each other. A glass slab of thickness t and refractive index n₀ is centered between them, and a monochromatic point source S is embedded at the slab center on the common axis. For the image to form on S itself, which mirror separations are correct? Image
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Question

Two identical concave mirrors of focal length f face each other. A glass slab of thickness t and refractive index n₀ is centered between them, and a monochromatic point source S is embedded at the slab center on the common axis. For the image to form on S itself, which mirror separations are correct? Image

Select all that apply

G1 Physics · Accepted Answer

For axial paraxial rays, a slab of thickness t replaces an equal air thickness by an effective optical distance t/n₀. Therefore the mirror separation gets the correction Δ = t − t/n₀ = (1 − 1/n₀)t. Two self-imaging possibilities occur: 1) S is effectively at the center of curvature of each mirror: separation = 4f + Δ. 2) S is effectively at the common focal arrangement of the two mirrors: separation = 2f + Δ. Thus A and B are correct.