In an experiment, you use the following setup with a converging lens C, to measu

Question

In an experiment, you use the following setup with a converging lens C, to measure the focal length of a diverging lens D. Let us call the distance, from the diverging lens, to the virtual image due to the diverging lens, s^+p Compute the focal length of the diverging lens use symbols as given and write appropriate equations, then use the numerical values to solve for the unknown variable. the object is 4.0 cm high, compute the expected size of the image on the screen. Is the final image inverted or upright? Use all the available information to draw a principal-rays diagram. Use the scale of 4.0 cm is equivalent to be 1.0cm.

Explanation / Answer

lens formula

1/v-1/u = 1/f , v is image distance, u object distance, f-focal length

we follow the convention , distance measured in direction of light are +ve

for the converging lens u is -ve

v, f are +ve

v = s' = 48 cm f = 16 cm

1/48 +1/u = 1/16

1/u = 1/16 -1/48 , u = 24 cm

image formed by the diverging lens is the object for the converging lens

u = v +d =v+20 = 24

v = 4 cm

for the diverging lens   u is -ve , behind the lens

                                     v is -ve , virtual image, f is -ve

u = s = -28 cm

-1/v +1/28 = -1/fD   

1/fD = 1/4 -1/28 = 6/28

fD = 4.67 cm, focallength of the diverging lens.

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