Question

The lens and mirror in Figure P23.51 are separated by 1.00 m and have focal lengths of +79.2 cm and -50.6 cm, respectively. If an object is placed 1.00 m to the left of the lens, locate the final image.

Answer 1

The location final image from the mirror, which is made when an object is placed 1.00 m to the left of the lens, is 0.58 right to the mirror.

What is the focal length of the lens?

The focal length of the lens is the length of the distance between the middle of the lens to the focal point.

It can be find out using the following formula as,

$-\dfrac{1}{v}+\dfrac{1}{u}=\dfrac{1}{f}$

Here, (v)is the distance of the image, (u) is the distance of the object, and (f) is the focal length of the lens.

The lens and mirror in the Figure are separated by 1.00 m and have focal lengths of +79.2 cm and -50.6 cm, respectively. Change the units of focal length in meters,

$f_l=79.2\text{ cm=0.792 m}\\f_m=-50.6\text{ cm=0.506 m}$

An object is placed 1.00 m to the left of the lens. Put the value in the lens formula as,

$-\dfrac{1}{v_l}+\dfrac{1}{1}=\dfrac{1}{0.792}\\-\dfrac{1}{v_l}=\dfrac{1}{0.792}-1\\v_1=3.81$

The distance of the image made by lens is 3.81 meters. The distance of this image from the mirror is,

$u_2=3.81-1\\u_2=2.81\rm \; m$

This distance is work as object distance for the mirror. The focal length of mirror is -0.506 m. Thus, the location of the final image is,

$-\dfrac{1}{v_2}+\dfrac{1}{3.81}=\dfrac{1}{-0.506}\\\dfrac{1}{v_2}=-\dfrac{1}{3.81}-(-\dfrac{1}{0.506})\\v_2=-0.58$

Thus, the location final image from the mirror which is made when an object is placed 1.00 m to the left of the lens, is 0.58 right to the mirror.

Learn more about the focal length here;

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