A biconvex lens of central thickness 6.50 cm has air on its left side and water

Question

A biconvex lens of central thickness 6.50 cm has air on its left side and water on its right side. II has a radius of curvature of 10 cm on its left side and a radius of curvature of 20 cm on its right side. The glass of the lens obeys the Herzberger dispersion formula such that the index of refraction is wavelength dependent You'll need the fit results from the Herzberger dispersion curve to complete this problem (Assume the fit results from the prism glass also apply to this glass, and that the index of refraction of water is NOT wavelength dependent). Determine the separation distance between the red (650 nm) and violet (400 nm) focal points with respect to the vertices (v1 and v2) of this lens. Determine the locations of the six cardinal points of this lens for the wavelength at the midpoint of the wavelength range given in part a Make a SCALE DRAWING of the lens, showing the locations of all of the results of parts a and b. The Herzberger dispersion formula is n = A + B lambda^2 + C/(lambda^2 - lambda^2_0) + D/(lambda^2 - lambda^2_0)^2 And The Herzberger fit constant is A= 1 6041, B= -8 27830E-03, C= 5 97890E-03, D= 2 02190E-05, Lambda 0 =0 19748

Explanation / Answer

After fitting the values in the Herzberger dispersion formula, the values for the refractive index for red is 1.46408273635746 and that of violet comes out to be 1.46408273853137.

(a) The radius of curvature of the left side is 10cm. so, the focal length is 5cm. To find the focal length of the individual colours, multiply the refractive index by the focal length 5 .Similarly, for the right side, multiply the refractive index by 10. Subtract the thickness 6.5 from both the results. This will give you the distance between the vertices and the focal points.

(b) The mean of 400 and 650 is 525. Repeat the above exercise for 525 and you will locate the focal points. For the principal and nodal points, use the formula to calculate the same.

Please comment if you get stuck somewhere.

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