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Theory of glass slab

Answer» \tRefraction through rectangular glass slab with parallel faces:\tThe refraction takes place at both air-glass interface and glass-air interface has the following characteristics:\t\xa0\tWhen a light ray travels from air to glass, the angle of incidence is greater than angle of refraction as ray bends towards normal.When a light ray travels from glass to air, the angle of refraction (also called angle of emergent in case of glass) is greater than the angle of incidence of glass-air interface as ray of light bends away from the normal.If the angle of incidence is zero, i.e. the incident ray is normal to the interface, the ray of light continues to travel in the same direction after refraction.The angle of emergence and angle of incidence will be equal. Emergent ray is parallel to the incident ray along with original direction but it will be laterally displaced to the left of the incident ray.For the same angle of incidence, lateral displacement is proportional to the thickness of the glass slab.For the same thickness of glass slab, the lateral displacement is proportional to the angle of incidence.\t\tAIMTo trace the path of a ray of light passing through a rectangular glass slab for different angles of incidence. Measure the angle of incidence, angle of refraction, angle of emergence and interpret the result.MATERIALS REQUIREDDrawing board, drawing pins, three plane sheets of white paper, a rectangular glass slab, geometry instruments, and sharp pointed pins.THEORYThe refraction takes place at both air-glass interface and glass-air interface of a rectangular glass slab.\tWhen the light ray incident on air-glass interface (DC) obliquely, it bends towards the normal.\tThe refracted ray is incident obliquely on the second parallel surface inside the rectangular glass slab, i. e. glass-air interface (AB) and after refraction, it moves away from the normal.\tThese refractions at both the surfaces obey the laws of refraction (Refer to basic building concept).\tPROCEDURE\tFix a white paper on a drawing board with the help of drawing pins and divide the sheet in two parts by a vertical line.\tPlace a rectangular glass slab in the first part. Draw its boundary. Remove the glass slab and label the boundary as A1, B1, C1, D1\xa0as shown below.\t\tDraw a normal (perpendicular) MN on the side A1B1\xa0at a point O1, slightly away from the centre towards A1\tDraw an oblique line P1Q1\xa0(incident ray) such that ∠P1O1M = 30° (Angle of incidence). Fix two sharp pointed pin P1\xa0and Q1\xa0vertically erected on the line P1O1\xa0at a distance of 4 to 6 cm apart.\tPlace the glass slab again within its boundary. Look at the feet of pins (not their heads) P1\xa0and Q1from the other parallel opposite face of the slab, i.e. from C1D1\xa0along the plane of paper. Fix other two pins R1\xa0and S1\xa0in such a way that R1\xa0, S1\xa0and the image of P1\xa0and Q1\xa0lie on a same straight line.\tRemove the glass slab and all the four pins. Encircle all the prick of the four pins. Join the points R1and S1\xa0within the encircle and produce upto the edge C1D1. Let R1S1\xa0meet C1D1\xa0at O1. This will act as an emergent ray.\tDraw a normal M1N1\xa0at O2. Join O1\xa0and O2. It will represent the path of ray inside the glass slab, i.e. refracted ray.\tMeasure the angle of emergence, i.e. ∠e = ∠N1O1S1\xa0and angle of refraction, i.e. ∠r = ∠NO1O2\tRepeat the experiment by taking the different angles of incidence such as 45° and 60° on the other part of paper and measure the angle of refraction and emergence accordingly and tabulate them.OBSERVATION TABLERESULT\tAt the point of incidence the incident ray, refracted ray and the normal to the air-glass interface, all lie in the plane of paper.\tWithin experimental limits, the angle of emergence and angle of incidence are equal.\tThe emergent ray is parallel to the incident ray.\tEmergent ray is laterally displaced.\tWhen the light ray travels from optically rarer medium (air) to optically denser medium (glass), the angle of refraction is less than the angle of incidence.\tThe refracted angle at the air-glass interface and the incident angle at the glass-air interface are found to be equal.\tFrom the observation table, it is clear that with the increase in angle of incidence, angle of refraction also increases.
Refraction through a rectangular glass slab:\xa0Consider a rectangular glass slab PQRS, as shown in figure below. On the face PQ, a ray AB is incident at an angle of incidence i1. It bends towards the normal, on entering the glass slab, and travels along BC inclined at an angle of refraction r1. The refracted ray BC is incident on the face SR at an angle of incidence i2. The emergent ray CD bends away from the normal at an angle of refraction r2.\xa0Now, using Snell’s law, we have\xa0Refraction from air to glass at face PQ,\xa0 ...(1)\xa0where,\xa0na\xa0is the refractive index of sir andng\xa0is the refractive index of glass.\xa0Fig.\xa0Refraction through a glass slab\xa0Using Snell’s law for refraction from glass to air at face SR, we have\xa0But Therefore, ...(2)\xa0Multiplying equations (1) and (2), we get\xa0\xa0\xa0i.e., \xa0Thus, the emergent ray CD is parallel to the incident ray AB, but it has been laterally displaced by a perpendicular distance CN with respect to the incident ray. This lateral shift in the path of light on emerging from a medium with parallel faces is called\xa0lateral displacement.It is found that the lateral displacement is directly proportional to the thickness of the glass slab.\xa0


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