Question

How would i find the image distance given object distance, two radii of curvatures, and index of refraction? (See details below)

The question asks to find the image distance given that the object distance is `6.5cm`, a thin lens with two radii: `r_1=+10` and `r_2=-10` and the index of refraction is `1.5` Also the object is on the left side closest to `r_1`

I drew an image to represent this situation:

Answer 1

See the answer below...

`+3.94" cm"`

Explanation:

• The Lens maker Law for general lens is `color(red)(ul(bar(|color(green)(p=1/f=(mu-1)(1/R_1-1/R_2))|`

• Let's apply it....

  `1/f=(1.5-1)(1/10+1/10)`
  `=>1/f=0.5xx1/5`
  `=>f=10`

• The general formula of lens `color(red)(ul(bar(|color(green)(1/v-1/u=1/f)|` `" "u=`distance of the object from the lens`" ; "` `v=`distance of image from the lens.

• So, we get `color(red)(1/v-1/6.5=1/10)=>v=130/33=+3.94`

Hope it helps...
Thank you...