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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1 Answer
Morgan
May 19, 2017

#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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