Answer to Question #257098 in Optics for Sam

Question

An equiconvex lens having spherical surfaces of radius 10cm, a central thickness of 2cm, and a refractive index of 1.61 is situated between air and water (refractive index 1.33). An object 5cm high is placed 60cm in front of the lens surface. Determine:

(i)             The locations of the cardinal points for the lens (focal lengths in reference to the principal planes, principal and nodal points), and

(ii)           The position of the image from the second principal plane and its nature.

Use matrix methods.

Answer 1

1)

$\frac 1F=\frac{(n-1)d}{nR^2},$

$F=\frac{nR^2}{(n-1)d},$

$F=\frac{1.61\cdot 0.1^2}{0.61\cdot 0.02}=1.32~m,$

2)

$\frac{n_1}d+\frac{n_2}f=\frac 1F,\implies$

$f=\frac{n_2Fd}{n_1F-d},$

$f=\frac{1.32\cdot 0.6\cdot 1.33}{1\cdot 1.32-0.6}=1.46~m,$

$\Gamma=\frac fd=\frac Hh,\implies$

$H=h\frac fd,$

$H=0.05\cdot\frac{1.46}{0.6}=0.12~m.$