## Ray Optics and Optical Instruments

# Refraction and Refraction at Spherical Surfaces and by Lenses

- Refraction is the property that light changes its velocity from one medium to another medium.
- When light passes from one medium to another medium velocity and wave length changes but frequency remains constant
- The medium in which velocity of light is more is called an optically rarer medium.
- The medium in which velocity of light is less is called an optically Denser medium.
- Optically Rarer and denser media is relative concept
- When a ray of light goes from a rarer medium to denser medium it bends towards the normal (r < i)
- When a ray of light goes from a denser medium to rarer medium it bends away from normal (r > i).
- Snell’s law can be expressed as μ sin θ = const.
- Refractive index \tt \mu = \frac{C}{V} = \frac{speed \ of \ light \ in \ vacuum}{speed \ of \ light \ in \ medium}
- Snell’s law in vector form \tt \mu_{1} \left( \hat{i} \times \hat{n}\right) = \mu_{2} \left( \hat{r} \times \hat{n}\right)
- \tt \frac{\mu_{1}}{\mu_{2}} = \frac{V_{1}}{V_{2}} = \frac{\lambda_{1}}{\lambda_{2}}
- \tt \frac{\mu_{1}}{\mu_{2}} = \frac{t_{2}}{t_{1}} = \frac{\sin \theta_{2}}{\sin \theta_{1}}
- \tt \frac{\mu_{1}}{\mu_{2}} = \frac{x_{2}}{x_{1}} (x
_{1}, x_{2}= distances travelled in two media) - A ray of light travels a distance ‘x’ in time ‘t’ \tt \mu = \frac{ct}{x}
- Optical path is the distance travelled by light in vacuum in the same time in which it travels a given path length in a medium.
- Optical path = μ x (x = geometrical path length)
- Lateral shift in glass slab of thickness ‘t’. \tt shift = \frac{t \sin (i - r)}{\cos r} where, i = angle of incidence and r = angle of refraction
- When a glass slab of thickness “t”. In the path of a divergent or convergent beam then shift = \tt t \left(1 - \frac{1}{\mu}\right)
- If light enters form rarer to denser medium μ = tan i.
- If light enters from Denser to rarer medium μ = cot i
- When object in denser medium and observer in rarer medium. \tt \mu = \frac{Real \ depth}{Apparent \ depth}
- Apparent shift S = t \left(1 - \frac{1}{\mu}\right)
- When three different liquids are present shift \tt s = d_{1} \left(1 - \frac{1}{\mu_{1}}\right) + d_{2} \left(1 - \frac{1}{\mu_{2}}\right) + d_{3} \left(1 - \frac{1}{\mu_{3}}\right)
- When object in rarer medium and observer in denser medium \tt \mu = \frac{Apparent \ depth}{real \ depth}
- Shift s = t (μ – l)

### Refraction at spherical surfaces and by lenses

### REFRACTION: View from 1:20 in this Video

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1. Snell's Law : The ratio of sine of the angle of incidence to sine of angle of refraction (r) is a constant called refractive index

i.e., \frac{\sin i}{\sin r} = \mu (a constant). For two media, Snell's law can be written as _{1}\mu_{2} = \frac{\mu_{2}}{\mu_{1}} = \frac{\sin i}{\sin r}

2. Absolute refractive index : When light travels from vacuum to any transparent medium then refractive index of medium w.r.t. vacuum is called it's absolute refractive index, i.e., \tt _{vacuum}\mu_{medium} = \frac{c}{v}

3. If a light ray travels from medium (1) to medium (2), then Relative Refractive index _{1}\mu_{2} = \frac{\mu_{2}}{\mu_{1}} = \frac{\lambda_{1}}{\lambda_{2}} = \frac{\nu_{1}}{\nu_{2}}

4. When object is in denser medium and observer is in rarer medium

\tt \mu = \frac{Real \ depth}{Apparent \ depth} = \frac{h}{h'}

5. The divergent (or) convergent beam

\tt d = h - h' = \left[1 - \frac{1}{\mu}\right] h

6. object is in rarer medium and observer is in denser medium \tt \mu = \frac{h'}{h}

7. d = (μ − 1)h

8. Refraction From Spherical Surface

Refraction formula : \tt \frac{\mu_{2} - \mu_{1}}{R} = \frac{\mu_{2}}{v} - \frac{\mu_{1}}{u}

9. Lens Formula : The expression which shows the relation between u, v and ƒ is called lens formula. \frac{1}{f} = \frac{1}{v} - \frac{1}{u}

10. Relation between object and image speed : If an object moves with constant speed (V_{0}) towards a convex lens from infinity to focus, the image will move slower in the beginning and then faster. Also V_{i} = \left[\frac{f}{f + u}\right]^{2}\cdot V_{0}