White light is used in a Young's double slit experiment.
Question: White light is used in a Young's double slit experiment. Find the minimum order of the violet fringe $(\lambda=400 \mathrm{~nm})$ which overlaps with a red fringe $(\lambda=700 \mathrm{~nm})$. Solution:...
Read More →A source of light emitting light of wavelengths
Question: A source of light emitting light of wavelengths $480 \mathrm{~nm}$ and $600 \mathrm{~nm}$ is used in a double slit interference experiment. The separation between the slits is $0.25 \mathrm{~mm}$ and the interference is observed on a screen placed at $150 \mathrm{~cm}$ from the slits. Find the linear separation between the first maximum (next to the central maximum) corresponding to the two wavelengths. Solution:...
Read More →Find the angular separation between the consecutive bright
Question: Find the angular separation between the consecutive bright fringes in a Young's double slit experiment with blue-green light of wavelength $500 \mathrm{~nm}$. The separation between the slits is $2.0 \times 10^{-3} \mathrm{~m}$. Solution:...
Read More →In a Young's double slit experiment,
Question: In a Young's double slit experiment, two narrow vertical slits placed $0.800 \mathrm{~mm}$ apart are illuminated by the same source of yellow light of wavelength $589 \mathrm{~nm}$. How far are the adjacent bright bands in the interference pattern observed on a screen $2.00 \mathrm{~m}$ away? Solution:...
Read More →In a double slit interference experiment,
Question: In a double slit interference experiment, the separation between the slits is $1.0 \mathrm{~mm}$, the wavelength of light used is $5.0 \times 10^{-7} \mathrm{~m}$ and the distance of the screen from the slits is $1.0 \mathrm{~m}$. (a) Find the distance of the centre of the central maximum. (b) How many bright fringes are formed in one centimeter width on the screen? Solution:...
Read More →The separation between the consecutive dark fringes in
Question: The separation between the consecutive dark fringes in a Young's double slit experiment is $1.0 \mathrm{~mm}$. The screen is placed at a distance of $2.5 \mathrm{~m}$ from the slits and the separation between the slits is $1.0 \mathrm{~mm}$. Calculate the wavelength of light used for the experiment. Solution:...
Read More →Two narrow slits emitting light in phase are separated by
Question: Two narrow slits emitting light in phase are separated by a distance of $1.0 \mathrm{~cm}$. The wavelength of the light is $5.0 \times 10^{-7} \mathrm{~m}$. The interference pattern is observed on a screen placed at a distance of $1.0 \mathrm{~m}$. (a) Find the separation between the consecutive maxima. Can you expect to distinguish between these maxima? (b) Find the separation between the sources which will give a separation of $1.0 \mathrm{~mm}$ between the consecutive maxima. Soluti...
Read More →Differentiate each of the following w.r.t.
Question: Differentiate each of the following w.r.t. $x$ : (ii) $e^{\sqrt{x}}$ (iii) $\mathrm{e}^{-2 \sqrt{\mathrm{x}}}$ Solution:...
Read More →The speed of the yellow light in the certain liquid is
Question: The speed of the yellow light in the certain liquid is $2.4 \times 10^{8} \mathrm{~m} / \mathrm{s}$. Find the refractive index of the liquid. Solution:...
Read More →The index of refraction of fused quartz is
Question: The index of refraction of fused quartz is $1.472$ for light of wavelength $400 \mathrm{~nm}$ and is $1.452$ for light of wavelength $760 \mathrm{~nm}$. Find the speeds of light of these wavelengths in fused quartz. Solution:...
Read More →The wavelength of sodium light in air is
Question: The wavelength of sodium light in air is $589 \mathrm{~nm}$. (a) Find its frequency in air. (b) Find its wavelength in water (refractive index=1.33). (c) Find its frequency in water. (d) Find its speed in the water. Solution:...
Read More →Differentiate each of the following w.r.t.
Question: Differentiate each of the following w.r.t. $x$ : (i) $e^{4 x}$ (ii) $\mathrm{e}^{-5 \mathrm{x}}$ (iii) $(e)^{x^{3}}$ Solution:...
Read More →Find the range of frequency of light that is visible to an average
Question: Find the range of frequency of light that is visible to an average human being $(400 \mathrm{~nm}\lambda700 \mathrm{~nm})$. Solution:...
Read More →Solve this following
Question: If $y=\frac{(\cos x+\sin x)}{(\cos x-\sin x)}$, prove that $\frac{d y}{d x}=\sec ^{2}\left(x+\frac{\pi}{4}\right)$ Solution:...
Read More →Solve this following
Question: If $y=\frac{(\cos x-\sin x)}{(\cos x+\sin x)}$, prove that $\frac{d y}{d x}+y^{2}+1=0$ Solution:...
Read More →Solve this following
Question: Find $\frac{d y}{d x}$, when: $y=\frac{\left(\sin x+x^{2}\right)}{\cot 2 x}$ Solution:...
Read More →A source emitting a sound of frequency f is placed at a large distance
Question: A source emitting a sound of frequency $f$ is placed at a large distance from an observer. The source starts moving towards the observer with a uniform acceleration $a$. Find the frequency heard by the observer corresponding to the wave emitted just after the source starts. The speed of sound in the medium is $v$. Solution:...
Read More →A small source of sound S of frequency 500 Hz
Question: A small source of sound $S$ of frequency $500 \mathrm{~Hz}$ is attached to the end of a light string and is whirled in a vertical circle of radius $1.6 \mathrm{~m}$. The string just remains tight when the source is at the highest point. (a) An observer is located in the same vertical plane at a large distance and at the same height as the centre of the circle. The speed of sound in air $=330 \mathrm{~m} \mathrm{~s}^{-1}$ and $g=10 \mathrm{~m} \mathrm{~s}^{-2}$. Find the maximum frequen...
Read More →Solve this following
Question: Find $\frac{d y}{d x}$, when: $y=\sin \left(\frac{1+x^{2}}{1-x^{2}}\right)$ Solution: $y=\sin \left(\frac{1+\tan ^{2} a}{1-\tan ^{2} a}\right)$...
Read More →Differentiate each of the following w.r.t.
Question: Differentiate each of the following w.r.t. $x$ : $\cos 4 x \cos 2 x$ Solution:...
Read More →Differentiate each of the following w.r.t.
Question: Differentiate each of the following w.r.t. $x$ : $\sin 2 x \sin x$ Solution:...
Read More →Differentiate each of the following w.r.t.
Question: Differentiate each of the following w.r.t. $x$ : $\sin 5 x \cos 3 x$ Solution:...
Read More →A source of sound emitting a 1200 Hz note travels along a straight line
Question: A source of sound emitting a $1200 \mathrm{~Hz}$ note travels along a straight line at a speed of $170 \mathrm{~m} \mathrm{~s}^{-1}$. A detector is placed at a distance $200 \mathrm{~m}$ from the line of motion of the source. (a) Find the frequency of sound receive by the detector at the instant when the source gets closest to it. (b) Find the distance between the source and the detector at the instant in detects frequency $1200 \mathrm{~Hz}$. Velocity of sound in air $=340 \mathrm{~m}...
Read More →A source emitting sound at frequency
Question: A source emitting sound at frequency $4000 \mathrm{~Hz}$, is moving along the $Y$-axis with a speed of $22 \mathrm{~m} \mathrm{~s}^{-1}$. A listener is situated on the ground at the position $(660 \mathrm{~m}, 0)$. Find the frequency of the sound received by the listener at the instant the source crosses the origin. Speed of sound in air $=330 \mathrm{~m} \mathrm{~s}^{-1}$. Solution:...
Read More →Figure shows a source of sound moving along
Question: Figure shows a source of sound moving along $X$-axis at a speed of $22 \mathrm{~m} \mathrm{~s}^{-1}$ continuously emitting a sound of frequency $2.0$ $\mathrm{kHz}$ which travels in air at a speed of $330 \mathrm{~m} \mathrm{~s}^{-1}$. A listener $Q$ stands on the $Y$-axis at a distance of $330 \mathrm{~m}$ from the origin. At $t$ $=0$, the sources crosses the origin $P$. (a) When does the sound emitted from the source at $P$ reach the listener $Q$ ? (b) What will be the frequency hear...
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