An object 2.87 cm high is placed 19.9 cm from a convex mirror with a focal lengt

Question

An object 2.87 cm high is placed 19.9 cm from a convex mirror with a focal length of 7.70 cm.

(a) Find the position of the image.

Your response differs from the correct answer by more than 100%. cm

(b) Find the magnification of the mirror.


(c) Find the height of the image.

Your response differs from the correct answer by more than 100%. cm

Suppose the object is moved so it is 3.85 cm from the same mirror. Repeat parts (a) through (c).

(a) q =
What is the relationship between the image distance, the object distance, and the focal length for a mirror? cm

(b) M =  

(c) h' =  
What factors determine the size of the image? cm

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

Explanation / Answer

Given that :

object height, h0 = 2.87 cm

object distance, d0 = -19.9 cm

focal length, f = 7.7 cm

(a) position of the image is given as :

using a mirror formula,

1 / d0 + 1 / di = 1 / f

1 / di = 1 / (7.7 cm) + 1 / (19.9 cm)

1 / di = (27.6 / 153.23) cm

di = (153.23 / 27.6) cm

di = 5.55 cm

(b) magnification of the mirror is given as :

M = - di / d0

M = - (5.55 cm) / (-19.9 cm)

M = 0.27                    (since magnification is positive, so the image is erect and real upright)

(c) height of the image is given as ::

M = hi / h0

(0.27) = hi / (2.87 cm)

hi = 0.77 cm

Suppose the object is moved so it is 3.85 cm from the same mirror.

object distance, d0 = -3.85 cm

(a) position of the image is given as :

using a mirror formula,

1 / d0 + 1 / di = 1 / f

1 / di = 1 / (7.7 cm) + 1 / (3.85 cm)

1 / di = (1.65 / 4.235) cm

di = (4.235 / 1.65) cm

di = 2.56 cm

(b) magnification of the mirror is given as :

M = - di / d0

M = - (2.56 cm) / (-3.85 cm)

M = 0.66                    (since magnification is positive, so the image is erect and real upright)

(c) height of the image is given as ::

M = hi / h0

(0.66) = hi / (2.87 cm)

hi = 1.89 cm

The image is real upright.

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