91Ó°ÊÓ

The focal length of a lens indicates how strongly it converges or diverges light. It is the distance between the lens and its focus, where parallel rays of light converge (or appear to diverge from). The lens formula can be expressed as \( \frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i} \), where \( f \) is the focal length, \( d_o \) is the object distance, and \( d_i \) is the image distance.
In this exercise, the negative image distance tells us the image is virtual and on the same side as the object.
After substituting the given values, we found \( f = -48.0 \, \text{cm} \), indicating a diverging lens. A negative focal length characterizes lenses that spread out light rays, instead of bringing them together.

Magnification tells us how much larger or smaller the image is compared to the object. It is calculated using the formula \( m = \frac{h_i}{h_o} = \frac{d_i}{d_o} \), where \( h_i \) is the image height and \( h_o \) is the object height. For instance, in our example, the object was 8.50 mm tall.
The magnification was found to be \( m = -\frac{3}{4} \), meaning the image's height is three quarters that of the object, and its inverted position results in a negative value.
The greater the absolute value of magnification, the larger the image appears relative to the object.

• If \( m > 1 \), the image is larger than the object.
• If \( m = 1 \), the image and object have the same size.
• If \( m < 1 \), the image is smaller than the object.

A diverging lens, often called a concave lens, has at least one surface that curves inward.
This type of lens causes incoming parallel light rays to spread out as if they were emanating from a common point (the focal point) on the opposite side of the lens.
Diverging lenses are known for forming virtual images, as the rays appear to spread out from a point on the same side as the object.

• They have a negative focal length.
• Are used in applications such as correcting short-sightedness.

Understanding the behavior of diverging lenses helps in comprehending how optical instruments, such as cameras and glasses, manipulate light.

A virtual image is formed when light rays diverge, causing the image to appear on the same side as the object. In this case, the image cannot be captured on a screen because the light does not actually converge to create the image.
Virtual images, like the one in our problem, are erect if viewed through the lens but appear inverted due to calculated magnification. They typically have the following characteristics:

• Cannot be displayed on a screen.
• Appear where light rays only seem to converge.
• Commonly produced by diverging lenses and flat mirrors.

Understanding these images plays a crucial role in designing optical devices, training in optics lab practices, and solving optical puzzles.