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*What is a Lens?*

*A transparent medium bounded by two surfaces, at least one of the surface should be a curved, is said to be a lens and it is said to be THIN LENS, When there is a small gap between the two surfaces or lenses where the thickness are much less and considered negligible in comparison to the radius of curvature.*

### LENS MAKER'S FORMULA:

When a lens of refractive index n2 is placed in the medium of refractive index n1, and the radii of curvatures of lens are R1 and R2, then we can write

( n1/v)-(n1/u) = (n2-n1)[1/R1 - 1/R2]

dividing the equation by n1,

we get, 1/v - 1/u = (n2/n1 - 1)[1/R1 - 1/R2]

when the object is at infinity, u = infinity, and then the image distance v = f, then

lens maker's formula is 1/f = (n2/n1 - 1)[1/R1 - 1/R2]

1/f =(n-1)[1/R1 - 1/R2]

**LIMITATIONS OF LENS MAKER'S FORMULA :**- the lens should be thin to consider above formula and the medium is same on either side of the lens.

sign conventions:

for convex lens:

R1 is positive, R2 is negative and f is positive

for concave lens:

R1 is negative, R2 is positive and f is negative

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**PROBLEMS USING LENS FORMULA:**

**1. An object is placed at 8 cm from a lens of focal length 15 cm, then calculate the image distance and determine whether the image is real or virtual.**

**2. A student using a lens of focal length -15cm, and object is placed at 20 cm from it, then calculate how far the image is from the lens and find out the magnification. Conclude whether the image is real or virtual.**

**3. Calculate the image distance and determine whether the image is real or virtual when an object is placed at 20 cm, from a lens of negative focal length -10cm.**

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