A 3cm tall object is placed 40cm from a concave mirror with a focal distance of 16cm. The object is moved to 10cm 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
Morgan
Apr 21, 2017

#d_i=-80/3cm#

#m=8/3#

#h_i=8cm#

Explanation:

I assume that "lens" should be "mirror."

We can use the mirror equation to find the image distance:

#1/f=1/d_i+1/d_o#

Where #f# is the focal length, #d_i# is the distance from the mirror to the image, and #d_o# is the distance from the mirror to the object.

We can then use our values for #d_i# and #d_o# to calculate the magnification, which is given by the equation:

#m=(-d_i)/(d_o)#

And using the fact that

#m=(-d_i)/(d_o)=h_i/h_o#

we can solve for #h_i# and use the value we obtain for #m# as well as #h_o# to calculate:

#h_i=m*h_o#

We are given that:

#h_o=3cm#

#f=16cm#

#d_o=10cm#

#1.# Calculate #d_i#:

#1/f=1/d_i+1/d_o#

#=>1/d_i=1/f-1/d_o#

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

#=(1/16-1/10)^-1#

#=-80/3cm#

#~~ -26.7cm#

#2.# Calculate #m#:

#m=-d_i/d_o#

#=-((-80/3))/10#

#=80/30#

#=8/3#

#3.# Calculate #h_i#:

#m=h_i/h_o#

#=>h_i=m*h_o#

#=(8/3)(3)#

#=8cm#

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