Q&A - Ask Doubts and Get Answers
Q

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)
Views

Le the parabolic reflector opens towards the right.

So the equation of 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.

Exams
Articles
Questions