The main objective of this question is to find the **lens magnification**.This question uses the **concept of lens magnification**. Lens magnification is the **ratio** between the** height of the image** and the** height of the object**. It is **mathematically** represented as:\[m \space = \space \frac{h_i}{h_o}\]Where the **lens magnification** is m and h_i is the **height of the image** and h_o is the **height of the object**.

## Expert Answer

We are **given**:

**Height** of the object, $ h_o = 1.0 cm $.

**Height** of the image, $ h_o = \space 4.0 cm $.

We have to **find** the **lens magnification**.

We **know** that:

\[m \space = \space \frac{h_i}{h_o}\]

Where the **lens magnification** is m and h_i is the **height of the image** and h_o is the **height of the object**.

By putting the values, we get:

\[m \space = \space \frac{-4}{1}\]

We place a **minus sign** with image height as it shows that the **image is inverted**.

\[m \space = \space -4 \space\]

Thus, the **lens magnification** is $-4$.

## Numerical Answer

The **lens magnification** is $-4$ when the height of the **image** is $4 cm$ and the height of the **object** is $1 cm$.

## Example

Find the lens magnification when the height of the object is $1 cm$ and the height of the image is $5 cm$, $8 cm$, and $10 cm$.

We are **given**:

Height of the **object**, $ h_o \= 1.0 cm $.

Height of the **image**, $ h_o = 5.0 cm $.

We have to **find** the** lens magnification**.

We know that:

\[m \space = \space \frac{h_i}{h_o}\]

Where the **lens magnification** is m and h_i is the** height of the image** and h_o is the **height of the object**.

By **putting** the values, we get:

\[m \space = \space \frac{-5}{1}\]

We place a **minus sign** with **image height** as it shows that the** image is inverted**.

\[m \space = \space -5 \space\]

Thus, the **lens magnification** is $-5$.

Now **solving** for the** image height** of $8 cm$.

We are **given** that:

**Height** of the object, $ h_o = 1.0 cm $.

**Height** of the image, $ h_o = 8.0 cm $.

We have to find the **lens magnification**.

We** know** that:

\[m \space = \space \frac{h_i}{h_o}\]

Where the **lens magnification** is m and h_i is the **height of the image** and h_o is the **height of the object**.

By **putting** the values, we get

\[m \space = \space \frac{-8}{1}\]

We place a **minus sign** with** image height** as it shows that the **image is inverted**.

\[m \space = \space -8 \space\]

Thus the **lens magnification** is $-8$.

Now **solving for the image height** of $10 cm$.

We are **given** that:

**Height** of the **object**, $ h_o = 1.0 cm $.

**Height** of the **image**, $ h_o = 10.0 cm $.

\[m \space = \space \frac{-10}{1}\]

We **place** a minus sign with image height as it shows that the **image is inverted**.

\[m \space = \space -10 \space\]

**Thus,** the **lens magnification** is $-10$.