Establish the refraction formula for a thin lens: 1f = ( mu - 1 ) ( 1R1 - 1R2 )

Formula for refraction through spherical surface is:

μ/v - 1/μ = (μ-1)/R

Directions,path of ways and distances are shown in figure.Assuming radii of lens as R₁ and R₂. For the surface AB of radius R₁ of lens L the object is O and the image is I.

Substituting values in equation as per figure,

μ/v - 1/μ = (μ-1)/R₁

For the surface AB of radius of the lens, I is the object and I is the image.

Substituting values in the formula will give,

(1/μ)/v - μ/v = (1/μ-1)/R₂ (Here, 1/μ is the refractive index of air with respect to glass)

Now, multiplying with in each term and adding both the equation will give:

1/v-1/u=μ-1[ 1/R₁ -1/R₂]

And since according to lens formula, 1/v-1/u=1/f Thus,

1/f = (μ-1)[ 1/R₁ - 1/R₂ ]

Final Answer: Hence, 1/f = (μ-1)[ 1/R₁ - 1/R₂ ]