Gaussian Lens Equation

Gaussian Lens Equation
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Gaussian Lens Equation

Figure 114.4 is an illustration of the rays from an object being refracted by a convex lens with left radius of curvature R₁, right radius of curvature R₂ and focal length f.

(a) Express the focal length f, in terms of the radii of curvature and the refractive indices of the lens and the medium through which the refracted light travels.
(b) Calculate the distance of the image from the lens in terms of the distance of the object from the lens and the focal length of the lens
(c) Calculate the height of the image in terms of the height of the object, the distance of the object from the lens and the distance of the image from the lens.

The strings: S₇P₄A₄₁ (Motion - Linear Motion).

The math:
Pj Problem of Interest is of type motion (linear). Reflection, refraction and diffraction are consequences of the motion of light.

The Gaussian Lens Equation:
1/d_o + 1/d_i = (n_lens/n_medium - 1)(1/R₁ +1/R₂) = 1/f -------(1)
Where d_o is distance of object from lens
d_i is distance of image from lens
n_lens is refractive index of lens
n_medium is refractive index of medium
R₁ is left radius of curvature and R₂ right radius of curvation (negative if lens is concave)
f is focal length.

(a) From equation (1):
1/f = (n_lens/n_medium - 1)(1/R₁ +1/R₂)
= [(n_lens - n_medium)/n_medium][(R₁ + R₂)/(R₁R₂)]
So, f = [n_medium(R₁R₂)]/[(n_lens - n_medium)(R₁ + R₂)]

(b)From equation (1):
1/d_o + 1/d_i = 1/f
So, 1/d_i = 1/f - 1/d_o = (d_o - f)/(fd_o)
So, d_i = fd_o/(d_o - f)

(c) h_o = height of object
h_i = height of image.
By the similarity of the triangles formed by the height of object and the height of image:
h_i/d_i = h_o/d_o
So, h_i = d_i(h_o/d_o)

Math

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