Question

An object is placed 5.00 cm beyond the focal point of a convex lens whose focal length is 10.0 cm. If the object height is 3.0 cm, calculate the image height

Answer 1

2

Explanation:

In here if we are place object 5cm away from a convex lense that has focal length of 10cm. Image will be formed in same size of the object . And it's upright , virtual and magnified like normal hand lense. There for wee need to use lense equation to find the image distance to get magnification of the object

Magnification = image distance / object distance

M = V/U

By lense formula ,

1/v - 1/ u = 1/ f

1/v + 1/5 = 1/ 10 ( by adding sign convention )

V = -10 cm

Therefor magnification = V / U

= 10/5

= 2

Answer 2

6 cm

Step-by-step explanation:

The lens equation is :

`(1)/(f) =(1)/(d_(o))+(1)/(d_(i))`

where
`f` is the focal length,
`d_(o)` is the distance of the object and
`d_(i)` is the distance of the image.

To find the height of the image we first need to find the distance of the image
`d_(i)`, so we clear for it in the last equation:

`(1)/(di) =(1)/(f) -(1)/(d_(o))`

and since
`f=10cm` and
`d_(o)=5cm`

`(1)/(di) =(1)/(10) -(1)/(5)`

`(1)/(di) =-(1)/(10)`

so

`d_(i)=-10`

Now to find the height of the image we use the magnification:

`M=(h_(i))/(h_(o)) =-(d_(i))/(d_(o))`

where
`h_(i)` is the image height, and
`h_(o)` is the object height:
`h_(o)=3cm`

clearing fot
`h_(i)`:

`h_(i)=-(h_(o)d_(i))/(d_(o))`

substituting known values:

`h_(i)=-((3cm(-10cm)))/(5cm)=(30cm)/(5)=6cm`

The image height is 6cm.