A 2 cm tall object is placed 41 cm from a convex lens with a focal distance of 7 cm. The object is moved to 4cm from the same lens. How would you calculate the distance to the image from the lens, the magnification, and the height of the image?

Question

Amelia Adams · Accepted Answer

#h_i=14/3cm#

#u->"The object distance"=-4cm#

#f->"Focal length of convex lens"=+7cm#

#v->"Image distance"=?#

Lens equation

#color(red)(1/v-1/u=1/f)#

#=>1/v-1/(-4)=1/7#

#=>1/v=1/7-1/4=(4-7)/28=-3/28#

#=>v=-28/3#

#"Magnification"=m=v/u=(-28/3)/-4=7/3#

Once more

#"Magnification"="Height of image"/"Height of object"=h_i/h_o#

Given height of object #h_o=2cm#

#:.h_i/h_o=7/3=>h_i=h_o xx7/3=2xx7/3#

#h_i=14/3cm#

Xavier Adame · Answer

undefined Use the lens formula: $ \frac{1}{f} = \frac{1}{u} + \frac{1}{v} $

1. Calculate the image distance ($v$) using the lens formula.
2. Calculate the magnification ($m$) using the magnification formula: $m = -\frac{v}{u}$
3. Calculate the image height ($h'$) using the magnification: $h' = m \times h$