virtual, upright c. Di = 25.78 cm, M =-2.18 virtual, upright real, inverted f. n

Question

virtual, upright c. Di = 25.78 cm, M =-2.18 virtual, upright real, inverted f. none of the above . A shopper standing 1.5 m from a convex security mirror sees his image w agnification of 0.25. Determine the following. a. Location of his image D a. D -0.137 m b. D -0.299 m c. Di -0.375 m d. Di=0.548m e. none of the above b. Focal length fof the mirror a.f -0.3883 m b,f=-0.4565 m c,f=-0.5783 m d. f=-0.6215 m e. none of the above Radius of curvature R of the mirror (3 c. a. R =-0.7766 m b. R- -0.9130 m c, R =-1.1566 m d, R= 2.6152 m e. none of the above

Explanation / Answer

Given that,

distance of shopper = o = 1.5 meters (He is actually object in this case, that is why denoted as "o")

Magnification = M = 0.25

(a)We need to find the image distance. Let it be "i"

We know that,

M = -i/o = 0.25

-i/1.5 = 0.25 => i = -0.375

Hence, His image is at i = -0.375 m

(b)Let f be the focal length. We know that from lens equation:

1/f = 1/i + 1/o

f = i * o / i + o = -0.375 * 1.5 / (-0.375 + 1.5) = -0.5m

Hence, the focal length of the convex mirror = -0.5 meter.

(c)Let R be the radius of curvature. We know that,

R = 2 x f = 2 x -0.5 = -1 meters

Hence, radius of curvature = R = -1 meters.

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