Question

Determine the image distance and image height for a 5.00 cm tall object placed 20.0 cm from a double convex lens with a focal length of 15.0 cm.

Answer 1

Given:

the height of the object is

`h_0=5\text{ cm}`

The distance of the object is

`d_0=-20\text{ cm}`

The focal length of the lens is

`f=15\text{ cm}`

Required: the distance of the image and height of the image.

Step-by-step explanation:

the lens formula is given by

`(1)/(f)=(1)/(d_i)-(1)/(d_0)`

Plugging all the values in the above relation, we get:

`\begin{gathered} \frac{1}{15\text{ cm}}=(1)/(d_i)-\frac{1}{-20\text{ cm}} \\ (1)/(d_i)=\frac{1}{15\text{ cm}}-\frac{1}{20\text{ cm}} \\ (1)/(d_i)=\frac{4-3}{60\text{ cm}} \\ d_i=60\text{ cm} \end{gathered}`

Thus, the distance of the image is 60 cm.

now calculate the height of the image

we know that

`(h_i)/(h_0)=(d_i)/(d_0)`

substitute all the values in the above relation, we get:

`\begin{gathered} h_i=5\text{ cm}*(60)/(-20) \\ h_i=-15\text{ cm} \end{gathered}`

Thus, the height of the image is 15 cm.