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  • If a parabolic reflector is 20 cm in diameter and 5 cm deep, find the focus.

1. If a parabolic reflector is 20 cm in diameter and 5 cm deep, find the focus.

Answers (1)

best_answer

Let the parabolic reflector open towards the right.

So, the equation for parabolic reflector will be,

y^2=4ax

Now, since this curve will pass through the point (5,10) if we assume origin at the optical centre,

So, 

10^2=4a(5)

a=\frac{100}{20}=5

Hence, the focus of the parabola is,

(a,0)=(5,0).

Alternative Method: 

As we know, on any concave curve

f=\frac{R}{2}

Hence, focus 

f=\frac{R}{2}=\frac{10}{2}=5.

Hence, the focus is 5 cm right to the optical centre.

Posted by

Pankaj Sanodiya

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