A 2.3 cm tall statue is 15 cm in front of a convex mirror. The mirror radius of

Question

A 2.3 cm tall statue is 15 cm in front of a convex mirror. The mirror radius of curvature is 18 cm. How tall is the image produced by the mirror? A) 5.6 cm B) 1.2 cm C) 0.18 cm D) 6.5 cm E) 0.86 cm A 4.0 cm tall object is placed 60 cm away from a converging lens of focal length 30 cm. What is the nature and location of the image? A) The image is real, 2.5 cm tall, 30 cm on the same side as object. B) The image is virtual, 2.5 cm tall, 30 cm on the other side of the lens. C) The image is virtual, 2.0 cm tall, 15 cm on the other side of the lens. D) The image is virtual, 4.0 cm tall, 60 cm on the same side as object. E) The image is real, 4.0 cm tall, 60 cm on the other side of the lens. John's face is 20 cm in front of a concave spherical shaving mirror of focal length 30 cm. How large an image does he observe? A) half as large as his face B) of the same size as his face C) twice as large as his face D) three times as large as his face E) four times as large as his face

Explanation / Answer

(1) 1/f=1/u+1/v

R=2f=18 cm, f=9 cm

using the sign convention

1/9=1/(-15)+1/v

==> v=5.6 cm

(2) 1/f=1/u+i/v

1/30=1/60+i/v

==> v=60 cm

The image is real. 4.0 cm tall and 60 cm on the other side of the lens

Option-(E)

(3) Magnification=m=-d1/d0=+x ==>d1=-xd0

1/0.2+1/(-0.4)=1/f

==> f=0.4 m=40 cm

2) 1/f=1/u-1/v

==>v=60 and Magnification = 3

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