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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.

Sagot :

Given:

the height of the object is

[tex]h_0=5\text{ cm}[/tex]

The distance of the object is

[tex]d_0=-20\text{ cm}[/tex]

The focal length of the lens is

[tex]f=15\text{ cm}[/tex]

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

Explanation:

the lens formula is given by

[tex]\frac{1}{f}=\frac{1}{d_i}-\frac{1}{d_0}[/tex]

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

[tex]\begin{gathered} \frac{1}{15\text{ cm}}=\frac{1}{d_i}-\frac{1}{-20\text{ cm}} \\ \frac{1}{d_i}=\frac{1}{15\text{ cm}}-\frac{1}{20\text{ cm}} \\ \frac{1}{d_i}=\frac{4-3}{60\text{ cm}} \\ d_i=60\text{ cm} \end{gathered}[/tex]

Thus, the distance of the image is 60 cm.

now calculate the height of the image

we know that

[tex]\frac{h_i}{h_0}=\frac{d_i}{d_0}[/tex]

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

[tex]\begin{gathered} h_i=5\text{ cm}\times\frac{60}{-20} \\ h_i=-15\text{ cm} \end{gathered}[/tex]

Thus, the height of the image is 15 cm.