Question

# A ray of light is coming along the line y=b from the positive direction of xâˆ’ axis and strikes the concave mirror whose interaction with xâˆ’ plane is a parabola y2=4ax. Find the equation of the reflected ray. Assume a,b are positive.

A
(yb)(4a2b2)=(4ax+b2)
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B
(y+b)(4a2b2)=(4axb2)
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C
(y+b)(4a2+b2)=(4axb2)
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D
(yb)(4a2b2)=(4axb2)
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Solution

## The correct option is D (y−b)(4a2−b2)=−(4ax−b2)Reflected ray passes through focus of parabola (a,0) and (b24a,b)y=b,x=b24a⇒y−0x−a=b−0b24a−a⇒y−bx−b24a=b−0b24a−a⇒y−b(4ax−b2)=b(b2−4a2)⇒(y−b)(4a2−b2)=−b(4ax−b2)

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