Suppose you had a microscope with three lenses. The primary objective lens has a

Question

Suppose you had a microscope with three lenses. The primary objective lens has a focal length of 4.0 cm, and is placed 4.2 cm from the microscope slide to be viewed. The eyepiece consists of two lenses. The first is a diverging lens with focal length -7.2 cm, placed 15 cm from the objective lens. Finally, a converging lens is placed 2.0 cm from the diverging lens, and has a focal length of 5.0 cm. Construct a carefully scaled ray tracing of this microscope. Determine the final image distance from the third lens. 1.

Explanation / Answer

Calculation for primary lens-

1/o + /i = 1/f

1/4.2 + 1/i = 1/4 (As per data given in question)

1/i = 1/4 - 1/4.2

i = 4*4.2 / 0.2

i = 84 cm (Far away from Primary lens)

This image will work as a object for First diverging lens.

Now the first diverging lens is 15 cm away form primary objective lens so actual distance of object for diverging lens is 84-15 = 69 cm, than-

1/o + /i = 1/f

1/69 + 1/i = 1/-7.2

1/i = -1/7.2 - 1/69

i = - (69*7.2) / (69+7.2)

i = - (496.8 / 76.2)

i = -6.52 cm (Opposite side of diverging lens)

This image will work as a object for converging lens.

And converging lens is placed 2 cm away from diverging lens than actual distance of object for converging lens is -6.52 - 2 = -8.52 cm, than-

1/o + /i = 1/f

1/-8.52 + 1/i = 1/5

1/i = 1/5 + 1/8.52

i = 5*8.52 / 13.52

i = 3.15 cm

Final image distance is 3.15 cm away from 3rd lens.

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