A 39.5-cm-focal-length converging lens is 28.0 cm behind a diverging lens. Parallel light strikes the diverging lens. After passing through the converging lens, the light is again parallel.
What is the focal length of the diverging lens?

The focal length of the diverging lens with the given parameters is;

f = 11.5 cm  

       In ray diagrams in lenses, some basic rules are followed such as;

- The incident rays that are parallel on the lens must form the image at the focus of lens on an opposite side.

- The rays that originate from the focus of the lens will pass in parallel lines after there has been refraction through the lens.

        From the rules above, we can infer that the rays passing through the converging lens will become parallel rays after undergoing refraction on the condition that the rays originate from the focus of the lens.

       Therefore, in the focus of both converging and diverging lenses, there must be a common focus point that acts as the object point and image point for both lenses respectively.

Thus;

Focal length of diverging lens = Distance between lenses - focal length of converging lens

We are given;

Focal length of converging lens = 39.5 cm

Distance between lenses = 28 cm

Thus, the focal length of the diverging lens = 39.5 - 28

In conclusion, the focal length of the diverging lens = 11.5 cm

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The focal length of the diverging lens is -11.5 cm.

The given parameters;

The focal length of converging lens is the distance between the optical center and focus of the lens.

The focal length of diverging lens is usually negative because it causes the rays leaving the lens to be more divergent than they before entering the lens.

The focal length of lens affects the size of image formed.

The focal length of the diverging lens is calculated as follows;

d = 28 cm - 39.5 cm

d = -11.5 cm

Thus, the focal length of the diverging lens is -11.5 cm.

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because it says use -2,0,and 2 for x, we can plug those numbers into the equation. y/4=3/4(-2)+2   y/4= -1 1/2 +2 now to get x by itself, we can multiply each side by 4. y=-6+8 which equals y=2 when x=-2. now you can do the same thing with 0 and 2 as x. you get y=8 when x=0 and y=14 when x=2.

x   |   y

-2 |   2

0   |   8

2   |   14