1. Two converging lenses are separated by 23.00 cm. The focal length of each len

Question

1. Two converging lenses are separated by 23.00 cm. The focal length of each lens is 11.60 cm. An object is placed 36.80 cm to the left of the lens that is on the left. Determine the final image distance relative to the lens on the right.
cm


2. A diverging lens (f = -10 cm) is located 20.0 cm to the left of a converging lens (f = 31.5 cm). A 3.00 cm tall object stands to the left of the diverging lens, exactly at its focal point.

(a) Determine the distance of the final image relative to the converging lens.
cm

(b) What is the height of the final image (including proper algebraic sign)?
cm

Explanation / Answer

1)

The focal length of each lens is f = 11.6 cm

The seperation of the lenses is d = 23 cm

The object distanec u = 36.8 cm

The equation of the thin lens for the leftside lens is

1/f = 1/u + 1/v

1/11.6 = 1/36.8 + 1/v

v = 16.94 cm

The inage is formed onthe right side of the lens

this image will acts like object for the second lens placed at

u' = d - v

u' = 23-16.94

u' = 6.06 cm

The equation of the thin lens for the rightside lens is

1/f = 1/u + 1/v

1/11.6 = 1/6.06 + 1/v

v = -12.69 cm

The final image is formed at a distance 12.69 cm left from the lens on the right

2) a).

1/s + 1/s' = 1/f

1/10 + 1/s' = 1/(-10)

s' = -5 cm

u = 20 - s' = 20 - (-5) = 25 cm

1/u + 1/v = 1/F

1/25 + 1/v = 1/31.5

v = -121.154 cm (in front of converging lens)


(b).

M? = s'/s = -5/10 = -0.5

M? = v/u = (-121.154)/25 = -4.846

M_total = M? M? = (-0.5)(-4.846) = 2.423

height of final image is

h' = (M_total) h = (2.423)(3) = 7.269 cm

Thank you!

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