A ray of light is coming along the line which is parallel to y-axis and strikes a concave mirror whose intersection with the x-y plane is parabola (x-4)2=4(y+2). After reflection, the ray must pass through the point

Question

A ray of light is coming along the line which is parallel to y-axis and strikes a concave mirror whose intersection with the x-y plane is parabola (x-4)2=4(y+2). After reflection, the ray must pass through the point (A) (4,-1) (B) (0,1) (C) (-4,1) (D) None of these

Tardigrade Admin · Accepted Answer

The equation of axis of the parabola is

x - 4 = 0

which is parallel to

y

-axis. So the ray of light is parallel to the axis of the parabola. We know that any ray parallel to the axis of a parabola passes through the focus after reflection.

∴

The ray must pass through the point

(4, - 1)

.

Q. A ray of light is coming along the line which is parallel to y-axis and strikes a concave mirror whose intersection with the x−y plane is parabola (x−4)2=4(y+2). After reflection, the ray must pass through the point

(4,-1)

(0,1)

(-4,1)

None of these

The equation of axis of the parabola is x−4=0 which is parallel to y -axis. So the ray of light is parallel to the axis of the parabola. We know that any ray parallel to the axis of a parabola passes through the focus after reflection. ∴The ray must pass through the point (4,−1).

Q. A ray of light is coming along the line which is parallel to y-axis and strikes a concave mirror whose intersection with the $x - y$ plane is parabola $(x - 4)^{2} = 4 (y + 2)$ . After reflection, the ray must pass through the point

The equation of axis of the parabola is $x - 4 = 0$ which is parallel to $y$ -axis. So the ray of light is parallel to the axis of the parabola. We know that any ray parallel to the axis of a parabola passes through the focus after reflection.
$∴$ The ray must pass through the point $(4, - 1)$ .