A small object is 25.0 cm from a diverging lens as shown in the figure. A conver

Question

A small object is 25.0 cm from a diverging lens as shown in the figure. A converging lens with a focal length of 12.3 cm is 30.0 cm to the right of the diverging lens. The two-lens system forms a real inverted image 17.0 cm to the right of the converging lens. What is the focal length of the diverging lens? f=?

A small object is 25.0 cm from a diverging lens as shown in the figure. A converging lens with a focal length of 12.3 cm is 30.0 cm to the right of the diverging lens. The two-lens system forms a real inverted image 17.0 cm to the right of the converging lens. What is the focal length of the diverging lens? f=?

Explanation / Answer

the focal length of the converging lens is f1=12.4cm the final image position from the converging lens is i=17cm if o is the object distance for the converging lens then 1/f1=1/o+1/i    1/o=1/f1-1/i         =1/12.4-1/17     o=45.87cm thus the image position from the diverging lens is    q=30-45.87=-15.87cm and the image position from the diverging lens is p=25cm if f is the focal length of the diverging lens then 1/f=1/p+1/q      =1/25-1/15.87 hence the focal length is f=-43.47cm

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