B: Malus Law-This law states that the intensity of the polarised light transmitted through the analyser varies as the square of the cosine of the angle between the plane of transmission of the analyser and the plane of the polarizer.
\(I=I_0 \cos ^2 \theta\)
Brewster's Law or Polarisation by ReflectionBrewster discovered that when a beam of unpolarised light is reflected from a transparent medium (refractive index \(=\mu\) ), the reflected light is completely plane polarised at a certain angle of incidence (called the angle of polarisation \(\theta_{\mathrm{P}}\) ).
Interference of Light - When two waves of exactly same frequency travels in a medium, in the same direction simultaneously then due to their superposition, at some points intensity of light is maximum while at some other points intensity is minimum. This phenomenon is called Interference of light.
Total internal Reflection (TIR)-If a ray of light goes from denser to rarer medium it bends away from the normal and the angle of incidence in denser medium increases, the angle of refraction in rarer medium also increases.
GUJCET 2018
Ray Optics
282250
A printed page is kept pressed by a transparent cube of edge \(t\). The refractive index of the cube varies as \(\mu(z)=1+\frac{z}{t}\), where \(z\) is the vertical distance from bottom of the cube. If viewed from top, then the printed letters appear to be shifted by an amount
1 \((1-\ln 2) \mathrm{t}\)
2 \((2 \ln 2-1) \mathrm{t}\)
3 \(\frac{\mathrm{t}}{2 \ln 2}\)
4 \(\frac{2 \mathrm{t}}{3 \ln 2}\)
Explanation:
A: Assume an elementary strip 'dz' at height of thickness \(z\).
\(\text { Apparent height }=\frac{\text { Real height }}{R I}=\frac{d}{\mu(z)}\)
Both side integrate-
\(\begin{aligned}
\int \mathrm{dh}=\int_0^{\mathrm{z}}\left(\frac{\mathrm{t}}{\mathrm{t}+\mathrm{z}}\right) \mathrm{dz} \\
\mathrm{h}=[\mathrm{t} \ln (\mathrm{t}+\mathrm{z})]_0^2=[\mathrm{t}(\ln (1+\mathrm{t})-\ln (\mathrm{t}+0)] \\
\mathrm{h}=\mathrm{t} \ln \frac{2 \mathrm{t}}{\mathrm{t}}=\mathrm{t} \ln 2 \\
\Delta \mathrm{x}=\mathrm{t}-\mathrm{t} \ln 2 \\
\Delta \mathrm{x}=(1-\ln 2) \mathrm{t}
\end{aligned}\)
TS- EAMCET-07.05.2018
Ray Optics
282251
A beaker contains oil upto a height of \(28 \mathrm{~mm}\) and water upto of \(26 \mathrm{~mm}\). Find the apparent shift in position of the bottom of the beaker when viewed from the top \(\left(n_{\text {water }}=1.33 n_{\text {oil }}=1.4\right)\)
1 \(54 \mathrm{~mm}\)
2 \(32 \mathrm{~mm}\)
3 \(28 \mathrm{~mm}\)
4 \(14 \mathrm{~mm}\)
Explanation:
D: Given that,
Height of oil \(\left(\mathrm{h}_{\mathrm{o}}\right)=28 \mathrm{~mm}\)
Height of water \(\left(\mathrm{h}_{\mathrm{w}}\right)=26 \mathrm{~mm}\)
\(\mathrm{n}_{\mathrm{w}}=1.33, \mathrm{n}_{\mathrm{o}}=1.4\)
Net apparent depth \((\mathrm{d})=\frac{\mathrm{h}_{\mathrm{o}}}{\mathrm{n}_{\mathrm{o}}}+\frac{\mathrm{h}_{\mathrm{w}}}{\mathrm{n}_{\mathrm{w}}}\)
\(\text { (d) }=\frac{28}{1.4}+\frac{26}{1.33}=39.55 \mathrm{~mm}\)
Therefore, Shift \(=\) total depth \(-\mathrm{d}\)
\(=(28+26)-39.55 \sqcup 14 \mathrm{~mm} .\)
TS EAMCET (Medical)-02.05.2018
Ray Optics
282252
Considering the fact that the speed of light in glass is not independent of the colour of light which of the statement is true?
1 Violet light travels slower than red light
2 Violet light travels faster than red light
3 Violet light travels same as red light
4 Only white light will be travelling
Explanation:
A We know that, \(\mu=\frac{\mathrm{c}}{\mathrm{v}}\)
Or \(\quad \mathrm{v} \propto \lambda\) (wavelength)
And violet colour has minimum wavelength among all seven colours.
Hence, its speed is slower among all of them,
B: Malus Law-This law states that the intensity of the polarised light transmitted through the analyser varies as the square of the cosine of the angle between the plane of transmission of the analyser and the plane of the polarizer.
\(I=I_0 \cos ^2 \theta\)
Brewster's Law or Polarisation by ReflectionBrewster discovered that when a beam of unpolarised light is reflected from a transparent medium (refractive index \(=\mu\) ), the reflected light is completely plane polarised at a certain angle of incidence (called the angle of polarisation \(\theta_{\mathrm{P}}\) ).
Interference of Light - When two waves of exactly same frequency travels in a medium, in the same direction simultaneously then due to their superposition, at some points intensity of light is maximum while at some other points intensity is minimum. This phenomenon is called Interference of light.
Total internal Reflection (TIR)-If a ray of light goes from denser to rarer medium it bends away from the normal and the angle of incidence in denser medium increases, the angle of refraction in rarer medium also increases.
GUJCET 2018
Ray Optics
282250
A printed page is kept pressed by a transparent cube of edge \(t\). The refractive index of the cube varies as \(\mu(z)=1+\frac{z}{t}\), where \(z\) is the vertical distance from bottom of the cube. If viewed from top, then the printed letters appear to be shifted by an amount
1 \((1-\ln 2) \mathrm{t}\)
2 \((2 \ln 2-1) \mathrm{t}\)
3 \(\frac{\mathrm{t}}{2 \ln 2}\)
4 \(\frac{2 \mathrm{t}}{3 \ln 2}\)
Explanation:
A: Assume an elementary strip 'dz' at height of thickness \(z\).
\(\text { Apparent height }=\frac{\text { Real height }}{R I}=\frac{d}{\mu(z)}\)
Both side integrate-
\(\begin{aligned}
\int \mathrm{dh}=\int_0^{\mathrm{z}}\left(\frac{\mathrm{t}}{\mathrm{t}+\mathrm{z}}\right) \mathrm{dz} \\
\mathrm{h}=[\mathrm{t} \ln (\mathrm{t}+\mathrm{z})]_0^2=[\mathrm{t}(\ln (1+\mathrm{t})-\ln (\mathrm{t}+0)] \\
\mathrm{h}=\mathrm{t} \ln \frac{2 \mathrm{t}}{\mathrm{t}}=\mathrm{t} \ln 2 \\
\Delta \mathrm{x}=\mathrm{t}-\mathrm{t} \ln 2 \\
\Delta \mathrm{x}=(1-\ln 2) \mathrm{t}
\end{aligned}\)
TS- EAMCET-07.05.2018
Ray Optics
282251
A beaker contains oil upto a height of \(28 \mathrm{~mm}\) and water upto of \(26 \mathrm{~mm}\). Find the apparent shift in position of the bottom of the beaker when viewed from the top \(\left(n_{\text {water }}=1.33 n_{\text {oil }}=1.4\right)\)
1 \(54 \mathrm{~mm}\)
2 \(32 \mathrm{~mm}\)
3 \(28 \mathrm{~mm}\)
4 \(14 \mathrm{~mm}\)
Explanation:
D: Given that,
Height of oil \(\left(\mathrm{h}_{\mathrm{o}}\right)=28 \mathrm{~mm}\)
Height of water \(\left(\mathrm{h}_{\mathrm{w}}\right)=26 \mathrm{~mm}\)
\(\mathrm{n}_{\mathrm{w}}=1.33, \mathrm{n}_{\mathrm{o}}=1.4\)
Net apparent depth \((\mathrm{d})=\frac{\mathrm{h}_{\mathrm{o}}}{\mathrm{n}_{\mathrm{o}}}+\frac{\mathrm{h}_{\mathrm{w}}}{\mathrm{n}_{\mathrm{w}}}\)
\(\text { (d) }=\frac{28}{1.4}+\frac{26}{1.33}=39.55 \mathrm{~mm}\)
Therefore, Shift \(=\) total depth \(-\mathrm{d}\)
\(=(28+26)-39.55 \sqcup 14 \mathrm{~mm} .\)
TS EAMCET (Medical)-02.05.2018
Ray Optics
282252
Considering the fact that the speed of light in glass is not independent of the colour of light which of the statement is true?
1 Violet light travels slower than red light
2 Violet light travels faster than red light
3 Violet light travels same as red light
4 Only white light will be travelling
Explanation:
A We know that, \(\mu=\frac{\mathrm{c}}{\mathrm{v}}\)
Or \(\quad \mathrm{v} \propto \lambda\) (wavelength)
And violet colour has minimum wavelength among all seven colours.
Hence, its speed is slower among all of them,
B: Malus Law-This law states that the intensity of the polarised light transmitted through the analyser varies as the square of the cosine of the angle between the plane of transmission of the analyser and the plane of the polarizer.
\(I=I_0 \cos ^2 \theta\)
Brewster's Law or Polarisation by ReflectionBrewster discovered that when a beam of unpolarised light is reflected from a transparent medium (refractive index \(=\mu\) ), the reflected light is completely plane polarised at a certain angle of incidence (called the angle of polarisation \(\theta_{\mathrm{P}}\) ).
Interference of Light - When two waves of exactly same frequency travels in a medium, in the same direction simultaneously then due to their superposition, at some points intensity of light is maximum while at some other points intensity is minimum. This phenomenon is called Interference of light.
Total internal Reflection (TIR)-If a ray of light goes from denser to rarer medium it bends away from the normal and the angle of incidence in denser medium increases, the angle of refraction in rarer medium also increases.
GUJCET 2018
Ray Optics
282250
A printed page is kept pressed by a transparent cube of edge \(t\). The refractive index of the cube varies as \(\mu(z)=1+\frac{z}{t}\), where \(z\) is the vertical distance from bottom of the cube. If viewed from top, then the printed letters appear to be shifted by an amount
1 \((1-\ln 2) \mathrm{t}\)
2 \((2 \ln 2-1) \mathrm{t}\)
3 \(\frac{\mathrm{t}}{2 \ln 2}\)
4 \(\frac{2 \mathrm{t}}{3 \ln 2}\)
Explanation:
A: Assume an elementary strip 'dz' at height of thickness \(z\).
\(\text { Apparent height }=\frac{\text { Real height }}{R I}=\frac{d}{\mu(z)}\)
Both side integrate-
\(\begin{aligned}
\int \mathrm{dh}=\int_0^{\mathrm{z}}\left(\frac{\mathrm{t}}{\mathrm{t}+\mathrm{z}}\right) \mathrm{dz} \\
\mathrm{h}=[\mathrm{t} \ln (\mathrm{t}+\mathrm{z})]_0^2=[\mathrm{t}(\ln (1+\mathrm{t})-\ln (\mathrm{t}+0)] \\
\mathrm{h}=\mathrm{t} \ln \frac{2 \mathrm{t}}{\mathrm{t}}=\mathrm{t} \ln 2 \\
\Delta \mathrm{x}=\mathrm{t}-\mathrm{t} \ln 2 \\
\Delta \mathrm{x}=(1-\ln 2) \mathrm{t}
\end{aligned}\)
TS- EAMCET-07.05.2018
Ray Optics
282251
A beaker contains oil upto a height of \(28 \mathrm{~mm}\) and water upto of \(26 \mathrm{~mm}\). Find the apparent shift in position of the bottom of the beaker when viewed from the top \(\left(n_{\text {water }}=1.33 n_{\text {oil }}=1.4\right)\)
1 \(54 \mathrm{~mm}\)
2 \(32 \mathrm{~mm}\)
3 \(28 \mathrm{~mm}\)
4 \(14 \mathrm{~mm}\)
Explanation:
D: Given that,
Height of oil \(\left(\mathrm{h}_{\mathrm{o}}\right)=28 \mathrm{~mm}\)
Height of water \(\left(\mathrm{h}_{\mathrm{w}}\right)=26 \mathrm{~mm}\)
\(\mathrm{n}_{\mathrm{w}}=1.33, \mathrm{n}_{\mathrm{o}}=1.4\)
Net apparent depth \((\mathrm{d})=\frac{\mathrm{h}_{\mathrm{o}}}{\mathrm{n}_{\mathrm{o}}}+\frac{\mathrm{h}_{\mathrm{w}}}{\mathrm{n}_{\mathrm{w}}}\)
\(\text { (d) }=\frac{28}{1.4}+\frac{26}{1.33}=39.55 \mathrm{~mm}\)
Therefore, Shift \(=\) total depth \(-\mathrm{d}\)
\(=(28+26)-39.55 \sqcup 14 \mathrm{~mm} .\)
TS EAMCET (Medical)-02.05.2018
Ray Optics
282252
Considering the fact that the speed of light in glass is not independent of the colour of light which of the statement is true?
1 Violet light travels slower than red light
2 Violet light travels faster than red light
3 Violet light travels same as red light
4 Only white light will be travelling
Explanation:
A We know that, \(\mu=\frac{\mathrm{c}}{\mathrm{v}}\)
Or \(\quad \mathrm{v} \propto \lambda\) (wavelength)
And violet colour has minimum wavelength among all seven colours.
Hence, its speed is slower among all of them,
B: Malus Law-This law states that the intensity of the polarised light transmitted through the analyser varies as the square of the cosine of the angle between the plane of transmission of the analyser and the plane of the polarizer.
\(I=I_0 \cos ^2 \theta\)
Brewster's Law or Polarisation by ReflectionBrewster discovered that when a beam of unpolarised light is reflected from a transparent medium (refractive index \(=\mu\) ), the reflected light is completely plane polarised at a certain angle of incidence (called the angle of polarisation \(\theta_{\mathrm{P}}\) ).
Interference of Light - When two waves of exactly same frequency travels in a medium, in the same direction simultaneously then due to their superposition, at some points intensity of light is maximum while at some other points intensity is minimum. This phenomenon is called Interference of light.
Total internal Reflection (TIR)-If a ray of light goes from denser to rarer medium it bends away from the normal and the angle of incidence in denser medium increases, the angle of refraction in rarer medium also increases.
GUJCET 2018
Ray Optics
282250
A printed page is kept pressed by a transparent cube of edge \(t\). The refractive index of the cube varies as \(\mu(z)=1+\frac{z}{t}\), where \(z\) is the vertical distance from bottom of the cube. If viewed from top, then the printed letters appear to be shifted by an amount
1 \((1-\ln 2) \mathrm{t}\)
2 \((2 \ln 2-1) \mathrm{t}\)
3 \(\frac{\mathrm{t}}{2 \ln 2}\)
4 \(\frac{2 \mathrm{t}}{3 \ln 2}\)
Explanation:
A: Assume an elementary strip 'dz' at height of thickness \(z\).
\(\text { Apparent height }=\frac{\text { Real height }}{R I}=\frac{d}{\mu(z)}\)
Both side integrate-
\(\begin{aligned}
\int \mathrm{dh}=\int_0^{\mathrm{z}}\left(\frac{\mathrm{t}}{\mathrm{t}+\mathrm{z}}\right) \mathrm{dz} \\
\mathrm{h}=[\mathrm{t} \ln (\mathrm{t}+\mathrm{z})]_0^2=[\mathrm{t}(\ln (1+\mathrm{t})-\ln (\mathrm{t}+0)] \\
\mathrm{h}=\mathrm{t} \ln \frac{2 \mathrm{t}}{\mathrm{t}}=\mathrm{t} \ln 2 \\
\Delta \mathrm{x}=\mathrm{t}-\mathrm{t} \ln 2 \\
\Delta \mathrm{x}=(1-\ln 2) \mathrm{t}
\end{aligned}\)
TS- EAMCET-07.05.2018
Ray Optics
282251
A beaker contains oil upto a height of \(28 \mathrm{~mm}\) and water upto of \(26 \mathrm{~mm}\). Find the apparent shift in position of the bottom of the beaker when viewed from the top \(\left(n_{\text {water }}=1.33 n_{\text {oil }}=1.4\right)\)
1 \(54 \mathrm{~mm}\)
2 \(32 \mathrm{~mm}\)
3 \(28 \mathrm{~mm}\)
4 \(14 \mathrm{~mm}\)
Explanation:
D: Given that,
Height of oil \(\left(\mathrm{h}_{\mathrm{o}}\right)=28 \mathrm{~mm}\)
Height of water \(\left(\mathrm{h}_{\mathrm{w}}\right)=26 \mathrm{~mm}\)
\(\mathrm{n}_{\mathrm{w}}=1.33, \mathrm{n}_{\mathrm{o}}=1.4\)
Net apparent depth \((\mathrm{d})=\frac{\mathrm{h}_{\mathrm{o}}}{\mathrm{n}_{\mathrm{o}}}+\frac{\mathrm{h}_{\mathrm{w}}}{\mathrm{n}_{\mathrm{w}}}\)
\(\text { (d) }=\frac{28}{1.4}+\frac{26}{1.33}=39.55 \mathrm{~mm}\)
Therefore, Shift \(=\) total depth \(-\mathrm{d}\)
\(=(28+26)-39.55 \sqcup 14 \mathrm{~mm} .\)
TS EAMCET (Medical)-02.05.2018
Ray Optics
282252
Considering the fact that the speed of light in glass is not independent of the colour of light which of the statement is true?
1 Violet light travels slower than red light
2 Violet light travels faster than red light
3 Violet light travels same as red light
4 Only white light will be travelling
Explanation:
A We know that, \(\mu=\frac{\mathrm{c}}{\mathrm{v}}\)
Or \(\quad \mathrm{v} \propto \lambda\) (wavelength)
And violet colour has minimum wavelength among all seven colours.
Hence, its speed is slower among all of them,
