A 5 cm tall object is placed 68 cm from a convex mirror with a focal distance of -4 cm. The object is moved to 1cm from the same mirror. How would you calculate the distance to the image from the lens, the magnification, and the height of the image?

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A 5 cm tall object is placed 68 cm from a convex mirror with a focal distance of -4 cm. The object is moved to 1cm from the same mirror. How would you calculate the distance to the image from the lens, the magnification, and the height of the image?

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Answer 1 · 2017-05-19T02:17:08

$d_i=-4/5cm$

$m=4/5cm$

$h_i=4cm$

Explanation:

We can begin by using the mirror equation to calculate the distance from the image to the mirror.

$1/(f)=1/d_i+1/d_o$

where $f$ is the focal length of the mirror, $d_i$ is the distance from the image from the mirror, and $d_o$ is the distance from the object to the mirror.

We are given that $f=-4cm$ and $d_o=1cm$ , and we can use these values to solve for $d_i$ :

$=>d_i=(1/f-1/d_o)^-1$

$=(-1/4-1)^-1$

$=-4/5cm$

Therefore, the image is formed behind the mirror and is said to be a virtual image.

We can now use the values for $d_i$ and $d_o$ to calculate the magnification of the mirror:

$m=-d_i/d_o$

$=-((-4/5))/1$

$=4/5$

Therefore, the image formed is reduced compared to the object size and upright.

Finally, we can use the values for $m$ and $h_i$ to find the height of the object:

$m=h_i/h_o$

$=>h_i=m*h_o$

$=4/5*5$

$=4cm$

$:. d_i=-4/5cm, m=4/5cm, h_i=4cm$

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A 5 cm tall object is placed 68 cm from a convex mirror with a focal distance of -4 cm. The object is moved to 1cm from the same mirror. How would you calculate the distance to the image from the lens, the magnification, and the height of the image?

1 Answer

Explanation:

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