Differentiate each of the following w.r.t
Question: Differentiate each of the following w.r.t $x$ : Solution: To find: Value of $\sin ^{-1}\left\{\sqrt{\frac{1-\cos x}{2}}\right\}$...
Read More →A 3 cm tall object is placed at a distance of
Question: A $3 \mathrm{~cm}$ tall object is placed at a distance of $7.5 \mathrm{~cm}$ from a convex mirror of focal length $6 \mathrm{~cm}$. Find the location, size and nature of the image. Solution:...
Read More →A candle flame 1.6cm high is imaged in a hall bearing of
Question: A candle flame $1.6 \mathrm{~cm}$ high is imaged in a hall bearing of diameter $0.4 \mathrm{~cm}$. If the ball bearing is $20 \mathrm{~cm}$ away from the flame, find the location and the height of the image. Solution:...
Read More →Solve this following
Question: Prove that $\frac{d}{d x}\left\{2 x \tan ^{-1} x-\log \left(1+x^{2}\right)\right\}=2 \tan ^{-1} x$ Solution:...
Read More →A 1cm object is placed perpendicular to the principal
Question: A $1 \mathrm{~cm}$ object is placed perpendicular to the principal axis of a convex mirror of focal length $7.5 \mathrm{~cm}$. Find its distance from the mirror if the image formed is $0.6 \mathrm{~cm}$ in size. Solution:...
Read More →A concave mirror has a focal length of
Question: A concave mirror has a focal length of $20 \mathrm{~cm}$. Find the position or position of an object for which the image size is double of the object size. Solution:...
Read More →Solve this following
Question: If $y=\sin ^{-1}(\cos x)+\cos ^{-1}(\sin x)$, prove that $\frac{d y}{d x}=-2$ Solution:...
Read More →A concave mirror forms an image of
Question: A concave mirror forms an image of $20 \mathrm{~cm}$ high object on a screen placed $5.0 \mathrm{~cm}$ away from the mirror. The height of the image is $50 \mathrm{~cm}$. Find the focal length of the mirror and the distance between the mirror and the object. Solution:...
Read More →A concave mirror having a radius of curvature
Question: A concave mirror having a radius of curvature $40 \mathrm{~cm}$ is placed in front of an illuminated point source at a distance of $30 \mathrm{~cm}$ from it. Find the location of the images. Solution:...
Read More →Differentiate each of the following w.r.t.
Question: Differentiate each of the following w.r.t. $x$ : $\sqrt{\sin ^{-1} \mathrm{x}^{2}}$ Solution:...
Read More →Solve this following
Question: Differentiate each of the following w.r.t. $x$ : $e^{\tan ^{-1} \sqrt{x}}$ Solution:...
Read More →Differentiate each of the following w.r.t.
Question: Differentiate each of the following w.r.t. x: $\tan \left(\sin ^{-1} x\right)$ Solution:...
Read More →Differentiate each of the following w.r.t.
Question: Differentiate each of the following w.r.t. $x$ : $\tan ^{-1}(\cos \sqrt{x})$ Solution:...
Read More →Differentiate each of the following w.r.t.
Question: Differentiate each of the following w.r.t. $x$ : $\left(\cot ^{-1} x^{2}\right)^{3}$ Solution:...
Read More →A convex lens of diameter 8.0 cm
Question: A convex lens of diameter $8.0 \mathrm{~cm}$ is used to focus a parallel beam of light of wavelength $620 \mathrm{~nm}$. If the light be focused at a distance of $20 \mathrm{~cm}$ from the lens, what would be the radius of the central bright spot formed? Solution:...
Read More →Differentiate each of the following w.r.t.
Question: Differentiate each of the following w.r.t. $x$ : $\log \left(\sin ^{-1} x^{4}\right)$ Solution:...
Read More →Light of wavelength 560 nm goes through a pinhole
Question: Light of wavelength $560 \mathrm{~nm}$ goes through a pinhole of diameter $0.20 \mathrm{~mm}$ and falls on a wall at a distance of $2.00 \mathrm{~m}$. What will be the radius of the central bright spot formed on the wall? Solution:...
Read More →Plane microwaves are incident on long list having
Question: Plane microwaves are incident on long list having a width of $5.0 \mathrm{~cm}$. Calculate the wavelength of the microwaves if the first diffraction minimum is formed at $\theta=30^{\circ}$. Solution:...
Read More →A glass surface is coated by an oil film of uniform thickness
Question: A glass surface is coated by an oil film of uniform thickness $1.00 \times 10^{-4} \mathrm{~cm}$. The index of refraction of the oil is $1.25$ and that of the glass is $1.50$. Find the wavelengths of light in the visible region ( $400 \mathrm{~nm}-750 \mathrm{~nm}$ ) which are completely transmitted by the oil film under normal incidence. Solution:...
Read More →A parallel beam of white light is incident normally
Question: A parallel beam of white light is incident normally on a water film $1.0 \times 10^{-4} \mathrm{~cm}$ thick. Find the wavelength in the visible range ( $400 \mathrm{~nm}-750 \mathrm{~nm}$ ) which are strongly transmitted by the film. Refractive index of water $=1.33$. Solution:...
Read More →A parallel beam of light of wavelength
Question: A parallel beam of light of wavelength $560 \mathrm{~nm}$ falls on a thin film of oil (refractive index=1.4). What should be the minimum thickness of the film so that it strongly reflects the light? Solution:...
Read More →A soap film of thickness 0.0011mm appears dark
Question: A soap film of thickness $0.0011 \mathrm{~mm}$ appears dark when seen by the reflected light of wavelength $580 \mathrm{~nm}$. What is the index of refraction of the soap solution, if it is known to be between $1.2$ and $1.5$ ? Solution:...
Read More →Differentiate each of the following w.r.t.
Question: Differentiate each of the following w.r.t. $x$ : $\tan ^{-1}(\cot x)$ Solution:...
Read More →Consider the arrangement shown in figure.
Question: Consider the arrangement shown in figure. By some mechanism, the separation between the slits $\mathrm{S}_{3}$ and $\mathrm{S}_{4}$ can be changed. The intensity is measured at the point $\mathrm{P}$ which is common perpendicular bisector of $\mathrm{S}_{1} \mathrm{~S}_{2}$ and $\mathrm{S}_{3} \mathrm{~S}_{4}$. When $z=\frac{D \lambda}{2 d}$, the intensity measured at $P$ is $I$. Find this intensity when $z$ is equal to (a) $\frac{D \lambda}{2 d},(\mathrm{~b})^{\frac{3 D \lambda}{2 d}}...
Read More →Differentiate each of the following w.r.t.
Question: Differentiate each of the following w.r.t. $x$ : $\left(1+x^{2}\right) \tan ^{-1} x$ Solution:...
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