Question

A concave mirror (f₁ = 13.6 cm) and a convex mirror (f₂ = ?5.50 cm) are facing each other and are separated by a distance of 35.8 cm. An object is placed between the mirrors and is 17.9 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 (d_i2) produced by the convex mirror?.

Answer 1

Its given that,

focal length of concave mirror = f1 = 13.6 cm

focal length of convex mirror = f2 = -5.5 cm

seperation = 35.8 cm

object dist from each mirror =do1 =do2= 17.9 cm

lets frst find the image dist for concave mirror = di1

we know from lens formula that,

1/f1 = 1/di1 + 1/do1

di1 = do1 x f1 / (do1 - f1 ) = 17.9 x 13.6 / (17.9 - 13.6) = 56.61 cm

Hence di1 = 56.61 cm

Now, its given that the light is reflected first from the concave mirror and then from the convex, so in this case,

do2 = 56.61 cm

putting the values in

di2 = do2 x f2 / do2 - f2 = 56.61 x (-5.5) / (56.61 - (-5.5) = 320.595 / 63.79 = 5.023 cm

hence, di2 = 5.023 cms