Video Transcript
The following figure shows parallel light rays reflecting from a convex mirror. The distances between the red, labeled (3), green, labeled (2), and blue incident
rays, labeled (1), are equal. Which is greater, the angle between the blue incident ray labeled (1) and the blue
reflected ray labeled (1) or the angle between the green incident ray labeled (2)
and the green reflected ray labeled (2)? (A) The angle is greater for the green rays labeled (2). (B) The angle is greater for the blue rays labeled (1). (C) The angle is the same for the blue rays labeled (1) and the green rays labeled
(2).
This question is asking us about light rays reflected from a convex mirror. We are told that all the incident rays are parallel and that the distances between
the rays are the same. We’re being asked specifically here about the blue ray labeled as (1) and the green
ray labeled as (2). We need to work out how the angles between the incident and reflected rays compare
between these two. Let’s label this angle as 𝜃 sub 𝑏 for the blue ray. That’s this angle we’ve marked on the diagram between the blue incident ray and the
blue reflected ray. Similarly, we’ll label the equivalent angle for the green ray as 𝜃 sub 𝑔.
To help us compare these angles, we can remember how light rays reflect off a convex
mirror. We can recall that any incident light ray parallel to the optical axis of a convex
mirror will be reflected so that if we extend the reflected ray back on the far side
of the mirror, it will pass through the focal point. Let’s also recall that the focal point of a convex mirror is on this axis, halfway
between the surface of the mirror and the center of curvature. That is, the focal point of the mirror is this point here. We can extend the blue and green reflected rays back behind the mirror, knowing that
they will pass through this focal point.
Since both the incident light rays are parallel to the optical axis, then this angle
here between the extension of the blue reflected ray and the axis must be equal to
𝜃 sub 𝑏, the angle between the blue incident and reflected rays. Similarly, this angle between the extension of the green reflected ray and the axis
must equal the angle 𝜃 sub 𝑔 between the green incident and reflected rays. We can see here that this angle 𝜃 sub 𝑏 is larger than this angle 𝜃 sub 𝑔, since
the blue dashed line makes a steeper angle to the axis than the green dashed
line.
So we’ve found that 𝜃 sub 𝑏 is larger than 𝜃 sub 𝑔. And we know that these angles are the angles between the incident and reflected rays
for the blue and green light, respectively. Therefore, we have found that the angle between the incident and reflected light ray
is greater for the blue rays than that for the green rays. We can thus identify the correct answer as option (B). The angle is greater for the blue rays labeled (1).
