Aptitude Test Problems in Physics Science for Everyone by S Krotov ( PDFDrive.com )

308 Aptitude Test Problems in Physics

4.18. We decompose the velocity vector v of the

person into two components, one parallel to the

mirror, vo , and the other perpendicular to the

Vp OH

Fig. 243

mirror, v± , i.e. v = vii v 1 (Fig. 243). The

velocity of the image will obviously be v'

— v 1. Therefore, the velocity at which the

person approaches his ithage is defined as his

velocity relative to the image from the formula

vret = 2v^1 = 2v sin a.

4.19. Let 0 be the centre of the spherical surface

of the mirror, ABC the ray incident at a distance

BE from the mirror axis, and OB = R (Fig. 244).

From the right triangle OBE, we find that sin a =

h/R. The triangle OBC is isosceles since LABO =

LOBC according to the law of reflection, and

LBOC = LABO as alternate-interior angles.

Hence OD = DB = R/2. From the triangle ODC,

we obtain

R R 2

x_

2 cos a

(C is the point of intersection of the ray reflected

by the mirror and the optical axis).

For a ray propagating at a distance h 1 , the dis-

tance x 1 R/2, with an error of about 0.5% since

2 iiR 2 —lez