Lens Equation Analysis

Superior Essays
Introduction
A lens is an object that forms images by refracting light. The images formed can be magnified, real and virtual depending on what lens used and the set-up of the lens system. There are two types of lenses, converging and diverging lenses. Converging lenses cause parallel light rays to converge to a point. Diverging lenses cause parallel light rays to diverge. Typically converging lens are thicker in the middle and diverging lenses are thinner in the middle.
Lenses are used for many applications they are used in glasses to correct eyesight, cameras to focus and capture light to form images, telescopes and also magnifying glasses. The theory of lenses can be very complicated especially for multi lens system. However in the special
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The Lens Equation [1]
This equation was used in the analysis to find out the focal point of the lens used. This equation can be derived either by using geometry and trigonometry.
Figure 1 Ray diagram used to derive the thin lens equation
Figure 3 Ray diagram used to derive the thin lens equation
In Figure 2 the parallel light ray is shown. Also drawn on are two similar triangles for both triangles the angle shown is the same. This means that the tanθ is the same for each triangle; Tanθ=opp/adj=h_0/f=(-h_1)/(d_1-f)
Where h_0 is the object height, f is the focal length, h1 is the image height, d0 is the object distance and d1 is the image distance
For the triangle below the central axis a minus sign has been added. This is because both θ are assumed to be positive. However the image height is inverted and therefore negative so to keep both tanθ’s positive a minus sign has been added.
The same operation done above can also be done for the similar triangles in figure 3. Tanθ^ '=h_0/d_0 =(-h_1)/d_1
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This value was 0.67 error bars away from the estimated value of (19.5 ± 0.5) cm. Another result that can be obtained from the graph is the gradient. The expected gradient was -1 as can be seen in the above picture the gradient from the results was (-1.01 ± 0.02). This shows that the experiment is valid and performed accurately.
The second part of the experiment focuses on finding the refractive index of the bi-convex lens. This was achieved by using a spherometer. A spherometer measures the radius of a sphere. Both sides of the lens can be considered part of a sphere. The radii of each imaginary sphere can be measured and using the lens maker equation can be used to obtain the refractive index.
Image from “university of Sussex physics foundation year laboratory

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