[phy] 超難F.3 PHY!! (Light)

You have to draw a diagram showing the position of the image of the clock, which is at a distance of 4 m behind the mirror and at a height of 2.4 m above the floor.

In order to see the image of the clock, draw a line (a light ray) from the bottom of the clock image, passing through the bottom of the mirror and end up at the eye of Sam.

Draw a horizontal line from Sam's eye towards the wall image (this line is not a light ray, but is used for easy of calculation only)

Thus, the eye of Sam, the drawn light ray and the wall image, together with the horizontal line jsut drawn formed two similar triangles.

Therefore, by similar triangles,
(h-1.2)/1 = (2.4-1.2)/(4+1)
where h is the height of the mirror above floor

solve for h gives h = 1.44 m

(b) When Sam's eye is at 1.6 m above the floor, draw a light ray from Sam's eye, passing through the top of the mirror and end up at the wall image at a point A, say. Again, draw a horizontal line from Sam's eye towards the wall image and cut it at a point B, say. Thus, two similar triangles are formed.

Therefore, (1.44+0.4-1.6)/1 = AB/(4+1)
i.e. AB = 1.2 m

The point A is thus (1.2+1.6) m = 2.8 m above the floor, which is equal to the height of the top of the mirror above the floor. That is, Sam is able to see the whole mirror when he stands up.