RAY OPTICS AND OPTICAL INSTRUMENTS
Focal length: The distance between the pole and the principal focus of concave lens is called its focal length.
Radius of curvature: The radius of curvature of a concave lens is the radius of the sphere of which the lens is a part.
Focus:It is the point at which rays converge or from which they appear to diverge.
Principal focus: It is the point, at which rays parallel to the principal axis converge (in case of a concave lens), or from which they appear to diverge (in case of a concave lens).
- Optical density is a measure of the ability of a substance of transmit the light.
- Optical density is the ratio of speed of light in the two media.
- Mass density is the mass per unit volume.
Law1:The incident, the reflected ray and the normal all lie in the same plane.
Law2:The angle of reflection is always equal to the angle of incidence.
Power of a lens: Reciprocal of focal length of a lens is called power of the lens.
$$ \therefore P=\frac{1}{f}$$
Unit:Diopter (or) m-1
Ans. Distance of image from wall $(v)= -35 cm$
focal length $(f)= -10 cm$
$ from \,\, Mirror \,\, formula \,\, \frac{1}{u}=\frac{1}{f}-\frac{1}{v} $
$$\therefore \frac{1}{u}=\frac{1}{-10}-\frac{1}{-35}$$
$$ \frac{1}{u}=\frac{-25}{350} $$
$$ u= -14 cm$$
Distance of Object from Wall $= 35-14=21 cm $
Ans. $A=4^{\circ} \,,\, \: D_{m}=2.48^{\circ}\,\, μ=? $
$ For \, small \, angled \, Prism \,D_{m}=(μ-1)A$
$\therefore \mu=\frac{2.48}{4}+1$
$ \mu= 1.62$
Dispersion: The phenomenon of splitting of light into itsconstituentcolours is known as dispersion.
Violet colour gets more dispersed.
Ans. $f=-30\:cm \,,\, \: Magnification \: m= \frac{1}{10}$
$ For \, Cancave \, lens \, m=\frac{f}{f+u}$
$\therefore \frac{1}{10}=\frac{-30}{-30+u}$
$ Object \, distance = -270\, cm$
Myopia:The light form a distant object arriving at the eye lens may get converged at a point in front of the retina. This type of defect is called ‘myopia’ or near ‘sightedness’.
It can be corrected by using concave lens.
Hypermetropia: If the eye-lens focusses, the incoming light at a point behind the retina is called
hypermetropia or farsightedness.
This defect can be corrected by using a convergent lens or convex lens.
Ans. $\frac{1}{f}= \frac{1}{v}-\frac{1}{u} $
$\frac{1}{f}= \frac{1}{-50}-\frac{1}{-25} $
$\therefore \: f= 50\:cm$
Ans. Definition: It is an incidence angle for which refraction angle is equal to $90^{\circ}$ .
Total internal reflection: When an incident angle is greater than the critical angle $(i>i_{c})$then the total light is reflected into the same denser medium. This phenomenon is know as Total internal reflection.
1. As the light ray is travelling from denser medium to rarer medium the refracted ray moves away from the normal drawn at the point of incidence
of light ray.
2. As the angle of incidence in denser medium increases the angle of refraction in rarer medium increases. At one particular angle of incidence in denser
medium the refracted light ray just grazes out the interface of two media.For this the angle of incidence in denser medium is called critical angle.
3. When the light ray is travelling from denser to rarer medium and the angle of incidence is greater than critical angle$(i>i_{c})$ then the light ray is reflected back to the same denser medium. This phenomenon is called total internal reflection.
Ans. Due to scattering of light setting sun appear red.
According to Rayleigh's scattering law the amount of scattering $a\propto\frac{1}{{\lambda}^4}$ (Where $\lambda$-Wave length )
In constitutents colours in the Sun light, Red colour having more wave length than rest of colours. At sunset or sunrise the sun rays have to pass through a larger distance in the atmosphere.Most of the blue and other short wavelengths are removed by scattering.The least scattered light i.e., red reaching our eyes. Therefore, the sun looks reddish.
Ans. Rainbow:This is a phenomenon due to combined effect of dispersion, refraction and reflection of sunlight by spherical water droplets of rain.
1. Firstly, light refracted into from air to rain droplet.
2.Secondly, refracted ray get reflected in rain droplet internally.
3.Thirdly, after reflection again light refracted into from rain droplet to air , During this light get dispersed.according to order of wavelengths red is deviated less and emerges at angle $42^0$, violet is deviated more and emeges $40^0$.For other colours, angles lie in between these two values.
The secondary rainbow is also formed due to double internal reflection of sunlight in the rain drops.
- Mirages are formed due to total internal reflection of light.
- On hot summer days the air near the ground becomes hotter. Hence it becomes less dense.
- Light ray from a tall object passes through air with decreasing refractive index towards ground.
- So, the angle of incidence near the ground exceeds critical angle, as a result total internal reflection takes place.
- For a distant observer light appears to come from somewhere below ground. So the observer assumes that the light reflected from the ground like by a pool of water.
- This forms an inverted image of tall object and causes optical illusions to the observers. This phenomenon is known as “mirage”.
Ans. Formation of image:The object is adjusted within the principal focus of the convex lens to form the image at the near point. The image is virtual, erect and magnified as shown in figure. The image is on the same side as the object at the least distance of distinct vision.
Equation of linear magnification $$m= (1+\frac{D}{f})$$Working: A simple micro scope consist of a single convex lens fitted in a metal frame.The object is adjusted within the principal focus of the convex lens to form the image at the near point. The image is virtual, erect and magnified as shown in figure. The image is on the same side as the object at the least distance of distinct vision.
Ans. Focal Length: The distance between pole and focus of a concave mirror is focal length of a concave mirror.
R=2f Proof: .Consider a ray parallel to the principal axis striking the mirror at $M$. Then $CM$ will be perpendicular to the mirror at $M$. Let$ θ$ be the angle of incidence, and $MD$ be the perpendicular from $M$ on the principal axis. Then
$\angle MCP=\theta$and$\angle MFP=2\theta$
Now,$\tan\theta=\frac{\mathrm{MD}}{\mathrm{CD}}$ and tan 2$\theta=\frac{\mathrm{MD}}{\mathrm{FD}} \quad--(1)$
For small $\theta$, whtch ts true for paraxtal rays, tan$\theta\approx\theta$,
$\tan2\theta\approx2\theta.$ Therefore,$$\frac{\mathrm{MD}}{\mathrm{FD}}=2\frac{\mathrm{MD}}{\mathrm{CD}}$$$$FD= \frac {CD}2$$Therefore, FD$=f$and CD$=R.$Equatton (9.2) then gives$$f=R/2$$
Ans. Snell’s Law: The ratio of sine of angle of incidence to the sine of angle of refraction is constant.$$\mu=\frac{\sin(i)}{\sin(r)}$$
From quadrilateral AQNR$$\angle A+\angle\mathrm{AQN}+\angle\mathrm{ARN}+\angle{QNR}=360^{\circ}$$$$\angle A+90^{\circ}+ 90^{\circ}+\angle{QNR}=360^{\circ}$$$$\angle A +\angle{QNR}=180^{\circ}$$ From the trlangle QNR,$$r_{_1}+r_{_2}+\angle\mathrm{QNR}=180^{\circ}$$Compartng these two equattons, we get $$r_{_1}+r_{_2}=A\quad-----(1)$$The total deviation $\delta$ is the sum of devlattons at the two faces, $$\delta=(i-r_{_1})+(e-r_{_2})$$$$\therefore \delta=i+e-A\quad-----(2)$$When $\delta = D_{m}$, then $i= e$ and $r_{l}=r_{2}.$
from eq(1)and(2)
$2r=$A or $r=\frac{A}{2}$
$D_{\mathrm{m}}=2i-A$,or$i=(A+D_\mathrm{m})/2$
The refractive index of the prism is $$ \mu =\frac{\sin[(A + D_m)/2]}{\sin[A/2]}$$