If you observe clearly, you'll find that refraction explains it. The expression for the absolute refractive index of a medium would thus be: absolute refractive index=speed of light in vacuumspeed of light in the given medium=cv\text{absolute refractive index}=\dfrac{\text{speed of light in vacuum}}{\text{speed of light in the given medium}} = \dfrac{c}{v}absolute refractive index=speed of light in the given mediumspeed of light in vacuum=vc. Suppose we wish to find the angle x that the outgoing ray makes with the Note: As the speed of light is at its maximum in vacuum, the absolute refractive index always greater than 111. So, at some points the light rays get totally reflected internally and reach the eyes of an observer, creating the reflection of an object on the surface of the Earth. Solution: According to the question, we have: But we should note that not all of the rays get reflected internally because they may not have struck the surface at the required angle (as seen in the figure above). n1 and n2 are the two different mediums that will impact the refraction.θ1 is the angle of incidence; θ2 is the angle of refraction. Substituting the value of BCBCBC in the first equation, SL=Lateral Displacement (CK)=tsin(i1−r1)cosr1S_L=\text{Lateral Displacement }(CK)=t\dfrac{\sin(i_1-r_1)}{\cos r_1}SL=Lateral Displacement (CK)=tcosr1sin(i1−r1). But it's working is based on this simple phenomenon of total internal reflection. Of course, refraction can also occur in a non-rectangular object (indeed, the objects are constant for given media1. This is very useful as it is used in fiber glasses where total internal reflection helps in fast movement of wavelengths. The angle θ b is the angle relative to the normal. n1/n2 is greater than one, so that the angle r 1.33 sin 30 o = 1.00029 sin x. x = 41 o. Refraction certainly explains why fishing with a rod is a sport, while fishing with a spear is not 2. Find the refractive index of the medium. The angle θ b can be found by rearranging the formula: The question asks for the angle of the light beam in the diamond, relative to the surface. (Take speed of light in vacuum= 3×108m/s3 \times 10^8 m/s3×108m/s, Solution: Absolute refractive index of diamond is =speed of light in vacuumspeed of light in diamond∴cv=2.42 ⟹ v=c2.42 ⟹ v=3×1082.42v=1.24×108m/s=\dfrac{\text{speed of light in vacuum}}{\text{speed of light in diamond}}\quad\therefore\dfrac{c}{v}=2.42\\ \implies v=\dfrac{c}{2.42} \implies v=\dfrac{3 \times 10^8}{2.42} \\\boxed{v=1.24 \times 10^8 m/s}=speed of light in diamondspeed of light in vacuum∴vc=2.42⟹v=2.42c⟹v=2.423×108v=1.24×108m/s, Refraction of a ray of light in a glass slab. The angle beyond which light in a given medium undergoes total internal reflection is called the critical angle. boundary. This dependence is made explicit in Snell's Law via refractive indices, numbers which If you take a close look at an optical fibre you will observe that it consists of a thin transparent material, this is know as the core. The light ray can actually bend so much that it never goes Given that refractive index of the glass slab is 2\sqrt{2}2. Applying Snell's Law when the light is incident on the glass slab's surface, sini1sinr1=n=refractive index of glass\dfrac{\sin i_1}{\sin r_1}=n=\text{refractive index of glass}sinr1sini1=n=refractive index of glass. Solution: From the previous topics, we know: refractive index=sinisinr=1.5 (in this case)sinr=1.5sin60≈0.57735 ⟹ r=sin−1(0.57735)≈35.25∘\text{refractive index}=\dfrac{\sin i}{\sin r}=1.5\text{ (in this case)}\\\sin r=\dfrac{1.5}{\sin 60}\approx 0.57735\\\implies r = \sin^{-1}(0.57735)\approx 35.25^\circrefractive index=sinrsini=1.5 (in this case)sinr=sin601.5≈0.57735⟹r=sin−1(0.57735)≈35.25∘, Now, applying the values in the formula for lateral displacement we get: SL=0.25cos(35.25)×sin(60−35.25)≈0.1281m=12.81cmS_L=\dfrac{0.25}{\cos(35.25)}\times\sin(60-35.25)\approx 0.1281 m =\boxed{12.81cm}SL=cos(35.25)0.25×sin(60−35.25)≈0.1281m=12.81cm. &=0.2\times \dfrac 13= 0.066m beyond the boundary between the two media. Surrounding the substance of unknown critical angle will consequently be reflected from the boundary instead of being refracted. Solution: We know that i^=45∘\hat i=45^{\circ}i^=45∘ and r^=30∘\hat r=30^{\circ}r^=30∘, Therefore refractive index, refracted ray make with the normal to the surface at the point of refraction. Optical fibers are devices used for guiding light in many applications, most notably for fast communication. When the light from any object (normally ships) reaches an observer, it undergoes a series of refractions which makes the light rays bend away from the normal, and at a point, they reach a stage where the angle incidence is greater than the critical angle and thus the rays undergo total internal reflection and reach the eye of an observer and creates and optical illusion that the object is really floating in the sky!

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