Physics Ray Optics and Optical Instruments

1/f_lens = (1.5/ (4/3) - 1) ( - 2/15) = f_lens = -60cm
∴ 1/fe = 2/ (-60) + 2/ (-15) => fe = -6 cm
∴ V = (14 * (-6)/ (14 + 6) = 4.2 cm from lens (virtual)

$F_{\text{convex}}=f$

${\mathrm{F}}_{\text{concave}}=-\mathrm{f}$

$\begin{array}{rr}& \frac{1}{{\mathrm{f}}_{\text{comb}}}=\frac{1}{{\mathrm{F}}_{\text{convex}}}+\frac{1}{{\mathrm{F}}_{\text{concave}}}\\ & =\frac{1}{\mathrm{f}}-\frac{1}{\mathrm{f}}\end{array}$

$\Rightarrow {\mathrm{f}}_{\text{comb}}=\mathrm{\infty }$

$\frac{1}{{\mathrm{f}}_1}=(1.6-1)\left(\frac{1}{\mathrm{\infty }}-\frac{1}{20}\right)=-\frac{3}{100}$

$\frac{1}{{\mathrm{f}}_2}=(1.5-1)\left(\frac{1}{20}-\frac{1}{-20}\right)$ $=\frac{1}{20}$

$\frac{1}{f_3}=\frac{1}{f_1}=-\frac{3}{100}$

$\frac{1}{{\mathrm{f}}_{\text{net}}}=\frac{1}{{\mathrm{f}}_1}+\frac{1}{{\mathrm{f}}_2}+\frac{1}{{\mathrm{f}}_3}$

$=-\frac{3}{50}+\frac{1}{20}$

$\Rightarrow {\mathrm{f}}_{\mathrm{n}\mathrm{e}\mathrm{t}}=-100\mathrm{c}\mathrm{m}$

Speed of light in air is

$\mathrm{C}=\frac{\mathrm{x}}{{\mathrm{t}}_1}$

Speed of light in another denser medium.

${\mathrm{C}}_2=\frac{10\mathrm{x}}{{\mathrm{t}}_2}$

$\Rightarrow \mu =\frac{C}{C_2}=\frac{x}{t_1}*\frac{t_2}{10x}$

$\Rightarrow \mu =\frac{{\mathrm{t}}_2}{10{\mathrm{t}}_1}$

For total internal reflection

$\mathrm{s}\mathrm{i}\mathrm{n}?\mathrm{C}=\frac{1}{\mu }$

$\Rightarrow \mathrm{s}\mathrm{i}\mathrm{n}?\mathrm{C}=\frac{10{\mathrm{t}}_1}{{\mathrm{t}}_2}$

$\mathrm{C}={\mathrm{s}\mathrm{i}\mathrm{n}}^{-1}?\left(\frac{10{\mathrm{t}}_1}{{\mathrm{t}}_2}\right)$

A total refractive prism is also known as a total internal reflection prism. It is an optical prism that is designed for reflecting 100% of the incident light. This happens since this prism uses the principle of total internal reflection. These prisms are oriented and shaped in a specific way so that the light that enters at a specific angle is completely reflected inside the prism. A right-angle prism, porro prism, dove prism and roof prism are some of the examples of total reflective prism. 

Total deviation in a prism is the total angle by which the light ray gets bent as it passes through the prism. It is an angle between incident ray and emergent ray of the prism. When a light enters the prism, it will bend towards the normal. After that, it will travel through the prism and bend away from the normal as it exits. Total deviation is the sum of these two from which the apex angle is subtracted.

The formula for total deviation for a prism is as follows:

$\delta = i_1 + e_2 - A$

• $i_1$ : angle of incidence at first surface
• $e_2$ : angle of emergence at second surface
• A: apex angle of the prism 

There are different types of glasses that are used in optical instruments, including the following:

• Crown glass (K): This glass is used in eyeglasses, microscopes and cameras. It is used in prisms and windows in optical systems. Crown glass has a low refractive index, low dispersion and excellent transparency in visible spectrum.

• Flint Glass (F): This glass, when combined with crown glass, can correct chromatic aberration in lenses. They are also used in prisms for spectroscopy.

• Extra-low dispersion glass: These glasses are used in premium optics that are also used for making high-quality camera lenses, telescopes and binoculars.