Light Question

Document Title

1. A mirror and a rectangular glass block of refractive index 1.56 are placed at right angle to each other. A laser beam strikes the mirror, 2 cm from point A with an angle of 50 deg to the mirror as shown in the Figure below. The figure is not drawn to scale.

                                    

(a) Determine
      (i) the angle of incidence at boundary AB.
      (ii) the angle of refraction at boundary AB.
(b) Explain whether total internal reflection occurs at boundary CD.
(c) Complete the path of the ray from point O until it emerges into the air again.

(a)(i) You have to first draw the reflected light ray at the mirror OA to boundary AB, then from there you can determine the angle of incidence at AB as 50o. Refer to (c).
(ii) n = sin(angle in air)/sin(angle in medium)
         1.56 = sin(50) / sin(r)
               r = 29.4o
(b) Analysis:
To determine whether total internal reflection occur or not, you have to check the following two conditions:
      (1) The light ray is from optically denser medium to less dense medium,
      (2) The angle of incidence is greater than critical angle.

By looking at the mediums, light ray is from optically denser medium to less dense medium. So first condition has satisfied.

      n = 1/sin(c)
1.56 = 1/sin(c)
      c = 39.9o
So, the critical angle is greater than the angle of incidence of 29.4o, which means second condition is not satisfied.

Answer:
      n = 1/sin(c)
1.56 = 1/sin(c)
      c = 39.9o
Since the critical angle is greater than the angle of incidence of 29.4o so that total internal reflection cannot occur at boundary CD.
(c)
                  

2. The Figure below shows an object AB and its image PQ being formed by a converging lens. XY is the principal axis. This diagram is drawn to scale.

                  

(a) On the Figure
      (i) draw two rays of light from the object to the image.
      (ii) locate the position of the lens and draw a straight line to present it.
      (iii) draw more rays, if necessary, to locate the position of the principal focus of the lens. Mark it by the symbol F.
(b) Describe the type and nature of the image.
(c) Find the linear magnification of the image.

(a) Analysis:
(i) One light ray from Tip of object to Tip of image;
      One light ray from Tail of object to Tail of image
(ii) When the above two light rays intersect, the intersection point is the position of the lens. Simply draw a vertical line with arrowhead to represent converging lens
(iii) To locate focus point, we have to draw either the second special light ray or the third special light ray. If you forget what they are, check them out.

Dont forget to include the arrowhead for light rays!

                  

(b) real, inverted and magnified
(c) Analysis:
Normally, to find the linear magnification, you just need to use a ruler to measure the height of object and image when the diagram is drawn to scale. However, in this question, we dont need to use ruler as the diagram is drawn on a grid box. So we can simply count it.

linear magnification = height of image / height of object = 8/4 = 2

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