Answer
Verified
323k+ views
- Hint: Use Snell’s law i.e. ${{\mu }_{1}}\sin i={{\mu }_{2}}\sin r$ , where $i$ is the angle of incidence and $r$ is the angle of refraction at the interface of the two mediums. ${{\mu }_{1}}$ is the refractive index of the medium where the light is incident and ${{\mu }_{2}}$ is the refractive index of the medium where the light gets refracted.
Complete step-by-step solution -
A glass slab is in cuboidal shape (opposite surfaces parallel to each other). Let us first understand what happens when a light ray enters a glass slab. When a light ray passes through a glass slab it is refracted twice at the two parallel faces and finally emerges parallel to its incident direction. Suppose a light ray enters the glass slab from air. It will first be refracted at this surface.
Use Snell’s law i.e. ${{\mu }_{1}}\sin i={{\mu }_{2}}\sin r$.
$\Rightarrow 1.\sin i=(1.5).\sin r$ …….(1) (Refractive indices of air and glass are 1 and 1.5 respectively)
Afterwards, the refracted ray will travel through the glass and will be incident on the opposite surface. Here, as you can see in the given figure, the angle of incident at surface 2 will be equal to the angle of refraction at surface 1 (since the normal at the two surfaces are parallel).
Let the angle of refraction at surface two be ‘e’. Now, use Snell’s law.
$\Rightarrow 1.\sin e=(1.5)\sin r$ …….(2)
Compare equations (1) and (2). We get, $i=e$. Hence, the emergent ray is parallel to the incident ray. The distance between these two rays is called the lateral displacement. Now, let us find an expression for the lateral displacement. For that, let the thickness of the glass slab be ‘t’.
As you can see in the given figure, $\vartriangle OMN$ is a right-angled triangle where MN is the lateral displacement. We have an expression for MN. In $\vartriangle OTM$ , $\sin \delta =\dfrac{MN}{OM}$
$\Rightarrow MN=OM\sin \delta $ ….(3).
In $\vartriangle OTM$ , $\cos r=\dfrac{OT}{OM}=\dfrac{t}{OM}$
$\Rightarrow OM=t\sec r$ ……(4).
Substitute the value of OM from equation (4) into equation (3).
$\Rightarrow MN=t\sec r.\sin \delta $ And $\delta =i-r$
$\Rightarrow MN=t\sec r.\sin \left( i-r \right)$
Therefore, we got the expression for lateral displacement. Now, if the light ray is incident normally on the surface, $i=0$. Hence, $r=0$. Therefore, MN will be zero. Meaning there will be any displacement in the ray of light.
Note: When a light ray falls on a glass slab, it is not that there will be a lateral displacement every time. One example you saw in the question. Another example is the internal reflection of the ray. The ray does refract into the outside medium, but it is reflected back into the same medium. This is only when the ray travels from a denser medium to a rarer medium.
Complete step-by-step solution -
A glass slab is in cuboidal shape (opposite surfaces parallel to each other). Let us first understand what happens when a light ray enters a glass slab. When a light ray passes through a glass slab it is refracted twice at the two parallel faces and finally emerges parallel to its incident direction. Suppose a light ray enters the glass slab from air. It will first be refracted at this surface.
Use Snell’s law i.e. ${{\mu }_{1}}\sin i={{\mu }_{2}}\sin r$.
$\Rightarrow 1.\sin i=(1.5).\sin r$ …….(1) (Refractive indices of air and glass are 1 and 1.5 respectively)
Afterwards, the refracted ray will travel through the glass and will be incident on the opposite surface. Here, as you can see in the given figure, the angle of incident at surface 2 will be equal to the angle of refraction at surface 1 (since the normal at the two surfaces are parallel).
Let the angle of refraction at surface two be ‘e’. Now, use Snell’s law.
$\Rightarrow 1.\sin e=(1.5)\sin r$ …….(2)
Compare equations (1) and (2). We get, $i=e$. Hence, the emergent ray is parallel to the incident ray. The distance between these two rays is called the lateral displacement. Now, let us find an expression for the lateral displacement. For that, let the thickness of the glass slab be ‘t’.
As you can see in the given figure, $\vartriangle OMN$ is a right-angled triangle where MN is the lateral displacement. We have an expression for MN. In $\vartriangle OTM$ , $\sin \delta =\dfrac{MN}{OM}$
$\Rightarrow MN=OM\sin \delta $ ….(3).
In $\vartriangle OTM$ , $\cos r=\dfrac{OT}{OM}=\dfrac{t}{OM}$
$\Rightarrow OM=t\sec r$ ……(4).
Substitute the value of OM from equation (4) into equation (3).
$\Rightarrow MN=t\sec r.\sin \delta $ And $\delta =i-r$
$\Rightarrow MN=t\sec r.\sin \left( i-r \right)$
Therefore, we got the expression for lateral displacement. Now, if the light ray is incident normally on the surface, $i=0$. Hence, $r=0$. Therefore, MN will be zero. Meaning there will be any displacement in the ray of light.
Note: When a light ray falls on a glass slab, it is not that there will be a lateral displacement every time. One example you saw in the question. Another example is the internal reflection of the ray. The ray does refract into the outside medium, but it is reflected back into the same medium. This is only when the ray travels from a denser medium to a rarer medium.
Recently Updated Pages
Basicity of sulphurous acid and sulphuric acid are
Assertion The resistivity of a semiconductor increases class 13 physics CBSE
Three beakers labelled as A B and C each containing 25 mL of water were taken A small amount of NaOH anhydrous CuSO4 and NaCl were added to the beakers A B and C respectively It was observed that there was an increase in the temperature of the solutions contained in beakers A and B whereas in case of beaker C the temperature of the solution falls Which one of the following statements isarecorrect i In beakers A and B exothermic process has occurred ii In beakers A and B endothermic process has occurred iii In beaker C exothermic process has occurred iv In beaker C endothermic process has occurred
The branch of science which deals with nature and natural class 10 physics CBSE
What is the stopping potential when the metal with class 12 physics JEE_Main
The momentum of a photon is 2 times 10 16gm cmsec Its class 12 physics JEE_Main
Trending doubts
Difference Between Plant Cell and Animal Cell
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
How do you solve x2 11x + 28 0 using the quadratic class 10 maths CBSE
Select the correct plural noun from the given singular class 10 english CBSE
What organs are located on the left side of your body class 11 biology CBSE
The sum of three consecutive multiples of 11 is 363 class 7 maths CBSE
What is the z value for a 90 95 and 99 percent confidence class 11 maths CBSE
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
How many squares are there in a chess board A 1296 class 11 maths CBSE