Question

An object is located 50 cm from a converging lens having a focal length of 15 cm. Which of the following is true regarding the image formed by the lens?It is virtual, inverted, and smaller than the object.

It is real, inverted, and larger than the object.
It is real, upright, and larger than the object.
It is virtual, upright, and larger than the object.
It is real, inverted, and smaller than the object.

Answer 1

It is real, inverted, and smaller than the object.

Step-by-step explanation:

First of all, we can use the lens equation to find the location of the image:

`(1)/(q)=(1)/(f)-(1)/(p)`

where

q is the distance of the image from the lens

f = 15 cm is the focal length (positive for a converging lens)

p = 50 cm is the distance of the object from the lens

Solving the equation for q,

`(1)/(q)=(1)/(15 cm)-(1)/(50 cm)=0.047 cm^(-1)\\q=(1)/(0.047 cm^(-1))=21.3 cm`

The distance of the image from the lens is positive, so we can already conclude that the image is real.

Now we can also write the magnification equation:

`{h_i}=-h_o (q)/(p)`

where
`h_i, h_o` are the size of the image and of the object, respectively.

Substituting p = 50 cm and q = 21.3 cm, we have

`{h_i}=-h_o (21.3 cm)/(50 cm)=-0.43 h_o`

So from this relationship we observe that:

`|h_i| < |h_o|` --> this means that the image is smaller than the object, and

`h_i < 0` --> this means that the image is inverted

so, the correct answer is

It is real, inverted, and smaller than the object.