A diverging lens of focal length $f_{1}$ is placed in front of and coaxially with a concave mirror of focal length $f_{2}$ . Their separation is d. A parallel beam of light incident on the lens returns as a parallel beam from the arrangement. Then

the beam diameters of the incident and reflected beams must be the same

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d = 2 | f_{2} | - | f_{1} |

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d = | f_{2} | - | f_{1} |

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if the entire arrangement is immersed in water, the conditions will remain unaltered

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Solution

The correct options are
A $d = 2 | f_{2} | - | f_{1} |$
D the beam diameters of the incident and reflected beams must be the same
the beam diameters of the incident and reflected beams must be the same
for the incident ray and the final ray to be parallel then the image formed by the lens must be at the center of the mirror
$| f_{1} | + d = 2 | f_{2} |$
$d = 2 | f_{2} | - | f_{1} |$
option $A, B$ are correct

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