Question

Establish the formula for a thin lens
1/f=(u-1) (1/R1-1/R2)

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Answer 1

Explanation:

Explanation is in The Photo given. ABOVE

Answer 2

Answer:  The answer will be 1/f = (n - 1) x (2/R)

Explanation: The formula for a thin lens is given by:

• 1/f = (n - 1) x ((1/R1) - (1/R2))

where: f is the focal length of the lens n is the refractive index of the lens material R1 is the radius of curvature of the first surface of the lens R2 is the radius of curvature of the second surface of the lens

The quantity (n-1) represents the refractive power of the lens, and (1/R1 - 1/R2) represents the power of the curved surfaces of the lens. The product of these two quantities gives the overall refractive power of the lens, which is equal to the reciprocal of the focal length of the lens.

So, the formula for a thin lens is:

• 1/f = (n - 1) x ((1/R1) - (1/R2))

A thin lens is a lens with a small thickness compared to its focal length. It is assumed that the lens is made of a material with a uniform refractive index, and that light passing through the lens travels in straight lines except at the point where it crosses the lens. The formula for a thin lens relates the focal length of the lens to the radii of curvature of its two surfaces and the refractive index of the lens material.

The formula for a thin lens is derived using the lensmaker's formula, which relates the focal length of a lens to the curvature of its surfaces and the refractive index of the lens material. The lensmaker's formula can be expressed as:

• 1/f = (n - 1) x ((1/R1) - (1/R2) + ((n - 1) x d)/n x R1 x R2)

where: f is the focal length of the lens n is the refractive index of the lens material R1 is the radius of curvature of the first surface of the lens R2 is the radius of curvature of the second surface of the lens d is the thickness of the lens

For a thin lens, the thickness d is much smaller than the radii of curvature R1 and R2, so the last term in the lensmaker's formula can be ignored. This gives us:

• 1/f = (n - 1) x ((1/R1) - (1/R2))

This is the formula for a thin lens that we were given to establish.

This formula tells us that the focal length of a thin lens is dependent on the curvature of its surfaces and the refractive index of the lens material. If the radii of curvature of the two surfaces are equal, the formula simplifies to:

• 1/f = (n - 1) x (2/R)

where R is the radius of curvature of each surface. This is known as the lensmaker's equation for a spherical lens.

In summary, the formula for a thin lens is derived from the lensmaker's formula and relates the focal length of the lens to the radii of curvature of its two surfaces and the refractive index of the lens material.

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