Describe the image of an object positions 20 cm from a concave spherical mirror

Question

Describe the image of an object positions 20 cm from a concave spherical mirror of radius 60 cm. Show your work, using the mirror equation 1/9 + 1/q = 1/f and magnification m = -a/p virtual, upright. 60 cm in front of mirror, magnified 3 times virtual, upright. 60 cm behind mirror, magnified 3 times virtual, upright. 60 cm behind mirror, magnified -3 times virtual, upright. 12 cm behind mirror, magnified 3 times 2. An object 7.0 high is placed 15 cm from a convex spherical mirror of radius 45 cm. Describe its image. Show your work, using the mirror equation 1/p + 1/q = 1/f and magnification m = - q/p virtual, upright. 9.0 cm behind mirror, 4.2 cm high virtual, upright. 45.0 cm behind mirror, 4.2 cm high virtual, upright. 9.0 cm behind mirror, 0.6 cm high virtual, inverted, 9.0 cm behind mirror, 4.2 cm high

Explanation / Answer

(1) and

Object distance p=20 cm

Radius r=60 cm

Focal length f =r/2=60/2 =30 cm

Now using the mirror equation

1/p+1/q = 1/f

1/20+1/q =1/30

1/q = 1/30 - 1/20 =20-30/600

1/q =-1/60

q=-60 cm

Object is virtual , up right 60 cm infront of mirror

Magnification m=- (-60)/20

= 3 times

(2)

Object height Ho =7cm

Object distance p=15 cm

Radius r=45 cm

Focal length f=r/2 =45/2 =22.5 cm

Now using mirror equation

1/p+1/q = 1/f

1/15+1/q=1/22.5

1/q=15-22.5/(22.5×15) =1/45

q=-45 cm

So the image is virtual , upright, 45 cm behind mirror

Now magnification m =Hi/Ho = - q/p

Hi/Ho = -(-45)/15

Hi/7 =3

Hi = 2×2.1 =4.2 cm

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