How to calculate magnification of lens?

Magnification of a lens is calculated by determining the ratio of the image size to the object size, or by relating image and object distances. According to the provided reference, magnification (m) can be calculated using the following formula:

m = h_i / h_o

Where:

• h_i represents the image height.
• h_o represents the object height.

In simpler terms, magnification is how much larger or smaller the image appears compared to the actual object.

Methods to Calculate Magnification

Here's a breakdown of how to calculate magnification using different methods:

1. Using Image and Object Heights

• Measure the Image Height (h_i): Determine the height of the image produced by the lens. This might be on a screen, a photograph, or within the lens itself (for virtual images).

• Measure the Object Height (h_o): Determine the actual height of the object you are viewing.

• Calculate the Ratio: Divide the image height by the object height.

  • Formula: m = h_i / h_o

  • Example: If an object is 1 cm tall (h_o = 1 cm) and its image through a lens is 3 cm tall (h_i = 3 cm), then the magnification is m = 3 cm / 1 cm = 3. This means the image is three times larger than the object.

2. Using Image and Object Distances

Magnification can also be determined by the ratio of image distance to object distance. This method requires you to know how far the object is from the lens and how far the image is formed from the lens. While not explicitly mentioned in the provided reference, it's a common and crucial aspect of magnification calculations.

• Measure the Image Distance (d_i): Determine the distance from the lens to the image.

• Measure the Object Distance (d_o): Determine the distance from the lens to the object.

• Calculate the Ratio: Divide the image distance by the object distance.

  • Formula: m = -d_i / d_o (Note the negative sign, which indicates image inversion. Real images are inverted, virtual images are upright)

  • Example: If an object is placed 10 cm from a lens (d_o = 10 cm) and the image is formed 20 cm from the lens (d_i = 20 cm), then the magnification is m = -20 cm / 10 cm = -2. This means the image is twice as large as the object and is inverted.

Practical Insights and Considerations

• Magnification can be positive or negative: A positive magnification indicates an upright (virtual) image, while a negative magnification indicates an inverted (real) image.
• Magnification values:
  • |m| > 1: Image is larger than the object (magnified).
  • |m| < 1: Image is smaller than the object (minified).
  • |m| = 1: Image is the same size as the object.
• Units: Magnification is a dimensionless quantity, meaning it doesn't have any units. It's simply a ratio.