Hi, really need help with A and exercise it part. EXAMPLE 23.3Images Formed by a

Question

Hi, really need help with A and exercise it part.

EXAMPLE 23.3Images Formed by a Convex Mirror

GOAL Calculate properties of a convex mirror.

PROBLEM An object 3.00 cm high is placed 20.0 cm from a convex mirror with a focal length of magnitude 8.00 cm. Find (a) the position of the image, (b) the magnification of the mirror, and (c) the height of the image.

STRATEGY This problem again requires only substitution into the mirror and magnification equations. Multiplying the object height by the magnification gives the image height.

SOLUTION

(A) Find the position of the image.

Because the mirror is convex, its focal length is negative. Substitute into the mirror equation.

Solve for q.

q = -5.71 cm

(B) Find the magnification of the mirror.

Substitute into the magnification equation.

(C) Find the height of the image.

Multiply the object height by the magnification.

h' = hM = (3.00 cm)(0.286) = 0.858 cm

LEARN MORE

REMARKS The negative value of q indicates the image is virtual, or behind the mirror. The image is upright because M is positive.

QUESTION Is the image that a convex mirror produces real or virtual?

PRACTICE IT

Use the worked example above to help you solve this problem. An object 2.89 cm high is placed 20.4 cm from a convex mirror with a focal length of 8.40 cm.

EXERCISEHINTS:  GETTING STARTED  |  I'M STUCK!

Suppose the object is moved so it is 4.20 cm from the same mirror. Repeat parts (a) through (c).

(a) q =  cm

(b) M =  

(c) h' =  cm

The image is  ---Select--- inverted and real inverted and virtual upright and real upright and virtual .

Explanation / Answer

(a)
f = - 8.40 cm
ho = 2.89 cm
do = 20.4 cm

1/f = 1/di + 1/do
-1/8.4 = 1/20.4 + 1/do
On solving
do = -5.95 cm

Position of the image = - 5.95 cm
-ve sign means the image is located behind the convex mirror

b)
M = -di/do
M = -(-5.95)/20.4
M = 0.3
Magnification , M = 0.3

c)
hi/ho = M
hi = M* ho
hi = 0.3*2.89 cm

height of image, hi = 0.867 cm

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