A concave mirror (f 1 = 14.6 cm) and a convex mirror (f 2 = 5.80 cm) are facing

Question

A concave mirror (f1= 14.6 cm) and a convex mirror (f2= 5.80 cm) are facing each other and are separated by a distance of 34.8 cm. An object is placed between the mirrors and is 17.4 cm from each mirror. Consider the light from the object that reflects first from the concave mirror and then from the convex mirror. What is the distance of the image (di2) produced by the convex mirror?

Please make sure you include the proper algebraic sign for the focal lengths, the distance of the objects, the distance of the images etc...

Explanation / Answer

here,

for concave mirror

f1 = 14.6 cm

object distance , do1 = 17.4 cm

let the image distance be d1

using the mirror formula

1/f1 = 1/di1 + 1/do1

1/14.6 = 1/di1 + 1/17.4

di1 = 90.73 cm

for convex mirror

object distance do2 = 34.8 - 90.73 = -55.93 cm

focal length , f2 = - 5.8 cm

let the image distance be di2

using the mirror formula

1/f2= 1/di2 + 1/do2

- 1/5.8 = 1/di2 - 1/55.93

di2 = - 6.47 cm

the the distance of the image (di2) produced by the convex mirror is - 6.47 cm

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