Sign up and receive the latest tips via email. Monday, 14 May 2018 Lens maker’s formula - Equation 1. u=∞ and v=f. (a) 0.667 (b) 1.5 (c) 0.5 (d) zero (e) data insufficient. A compound lens is a collection of simple lenses of different shapes and made of materials of different refractive indices, arranged one after the other with a common axis. The curved surfaces of a lens belong to two spheres. A relation between the focal length of a lens, radii of curvature of two surfaces and the refractive index of the material is called lens maker’s formula. common interests and common objectives are not necessary for society. Simple lenses are subject to the optical aberrations discussed above. 2 placed in a medium of refractive index ? The complete derivation of lens maker formula is described below. 1.Let R 1 and R 2 be the radii of curvature of two spherical surfaces ACB and ADB respectively and P be the … Lens Maker’s Formula (Refraction by a Lens) A relation between the focal length of a lens, radii of curvature of two surfaces and the refractive index of the material is called lens maker’s formula. 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The following formula, called the Lensmaker Equation, is used to determine whether a lens will behave as a converging or diverging lens based on the curvature of its faces and the relative indices of the lens material [n 1] and the surrounding medium [n 2]. 8. Suppose a ray OP parallel to the principle axis incident on the lens at a small height, h above it. This is lens maker’s formula. Using the Lens Maker’s Equation (3) and the appropriate sign for radii R1 and R2, determine the formulae for the focal distance of the hemisphere and the sphere in terms of R and n. Once you have these equations, you should be able to find n from the So for lens L1, we have, \begin{align*} \text {Object distance} = u \\ \text {Image distance} = v’ \\ \text {So, from lens formula,} \\ \frac {1}{f_1} &= \frac 1u + \frac {1}{v’} \dots (i) \end{align*}, When lens L2 is placed in contact, the image at I’ acts as virtual object for lens L2 since the converging beam is incident on L2 as shown in the figure, \begin{align*} \text {Object distance} = -v’ \\ \text {Image distance} = v \\ \text {So, from lens formula,} \\ \frac {1}{f_2} &= \frac {1}{-v’} + \frac {1}{v} \\ \frac {1}{f_2} &= \frac {1}{v} - \frac {1}{-v} \dots (ii) \\ \text {Adding equation} \: (i) \: \text {and} \: (ii) \\ \frac {1}{f_1} + \frac {1}{f_2} &= \frac {1}{u} + \frac {1}{v’} - \frac {1}{v’} + \frac {1}{v} \\ \frac {1}{f_1} + \frac {1}{f_2} &= \frac {1}{u} + \frac {1}{v} \dots (iii) \\ \end{align*}If F is the combined foal length of two thin lenses placed in contact having object distance u and image distance v, then\begin{align*} \frac 1F &= \frac {1}{u} + \frac {1}{v} \\ \text {From equation} \: (iii) \: \text {and} \: (iv) \\ \frac {1}{f_1} + \frac {1}{f_2} &= \frac 1F \\ \text {or,} \: \frac {1}{f_1} + \frac {1}{f_2} &= \frac 1F \\ \end{align*}. Lens, Thin Lens Formula Lens maker’s formula. Using the formula for refraction at a single spherical surface we can say that, For the first surface, For the second surface, Now adding equation (1) and (2), When u = ∞ and v = f. But also, Therefore, we can say that, Where μ is the refractive index of the material. In many cases these aberrations can be compensated for to a great extent by using a combination of simple lenses with complementary aberrations. 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Consider a thin convex lens of focal length f and refractive index µ. The angle of deviation is given by, \begin{align*} \tan \delta &= \frac hf \\\: \text {Since} \delta \: \text {is small,} \tan \delta = \delta, \text {and} \\ \delta &= \frac hf \dots (i) \\ \end{align*}, The portion PQ of the lens is a small angle prism which is formed by two tangent planes to the lens surfaces at P and Q.