How to find the net focal length when two lenses of different materials touch each other?The pair of lenses are surrounded by air.Please provide help according to the image attached.

To determine the net focal length of two lenses made from different materials that are in contact with each other and surrounded by air, we can use the lens maker's formula and the concept of equivalent focal lengths. Let's break this down step by step.

Understanding Lens Properties

Each lens has its own focal length, which depends on its curvature and the refractive index of the material. The lens maker's formula is given by:

f = (n - 1) * (1/R1 - 1/R2)

Where:

• f = focal length of the lens
• n = refractive index of the lens material
• R1 = radius of curvature of the first surface
• R2 = radius of curvature of the second surface

Calculating Individual Focal Lengths

For each lens, you will need to calculate its focal length using the lens maker's formula. Let’s say we have two lenses:

• Lens 1 with refractive index n1, radius of curvature R1a (for the first surface), and R1b (for the second surface).
• Lens 2 with refractive index n2, radius of curvature R2a (for the first surface), and R2b (for the second surface).

Using the lens maker's formula, you can find:

• Focal length of Lens 1: f1 = (n1 - 1) * (1/R1a - 1/R1b)
• Focal length of Lens 2: f2 = (n2 - 1) * (1/R2a - 1/R2b)

Combining the Focal Lengths

Once you have the individual focal lengths, you can find the net focal length (F) of the two lenses in contact. The formula for two thin lenses in contact is:

1/F = 1/f1 + 1/f2

This equation means that the reciprocal of the net focal length is equal to the sum of the reciprocals of the individual focal lengths.

Example Calculation

Let’s say:

• Lens 1 has a focal length of 10 cm (f1 = 10 cm).
• Lens 2 has a focal length of 20 cm (f2 = 20 cm).

Now, applying the formula:

1/F = 1/10 + 1/20

Calculating the right side:

1/F = 0.1 + 0.05 = 0.15

Now, taking the reciprocal to find F:

F = 1/0.15 ≈ 6.67 cm

Final Thoughts

This net focal length indicates how the two lenses work together as a system. Remember, the sign of the focal lengths matters too; if one lens is diverging (negative focal length), it will affect the overall focal length differently than two converging lenses. Always ensure to consider the nature of each lens when performing your calculations.