two lens of power 15d and +5D are placed is contact coaxially.the focal length of equivalent lens is :?

To find the focal length of two lenses placed in contact, we can use the lens formula for equivalent focal length. When two lenses are combined, the formula for the equivalent focal length (F) is given by:

Understanding the Formula

The formula for the equivalent focal length of two lenses in contact is:

1/F = 1/f1 + 1/f2

Where:

• F is the equivalent focal length of the combined lenses.
• f1 is the focal length of the first lens.
• f2 is the focal length of the second lens.

Identifying Focal Lengths

In your case, you have two lenses with powers of +15 diopters (D) and +5 diopters (D). The power (P) of a lens is related to its focal length (f) by the formula:

P = 1/f

From this, we can derive the focal lengths:

• For the first lens: f1 = 1/P1 = 1/15 D = 1/15 m = 0.0667 m (approximately 66.7 mm)
• For the second lens: f2 = 1/P2 = 1/5 D = 1/5 m = 0.2 m (200 mm)

Calculating the Equivalent Focal Length

Now that we have the focal lengths, we can substitute them into the equivalent focal length formula:

1/F = 1/f1 + 1/f2

Substituting the values:

1/F = 1/(0.0667) + 1/(0.2)

Calculating each term:

• 1/(0.0667) ≈ 15
• 1/(0.2) = 5

Now, adding these values together:

1/F = 15 + 5 = 20

Final Calculation

To find F, we take the reciprocal:

F = 1/20 = 0.05 m (or 50 mm)

Conclusion

The equivalent focal length of the two lenses placed in contact is 50 mm. This means that when these two lenses are used together, they will behave as a single lens with a focal length of 50 mm.