A mass m=50g is dropped on a vertical spring of spring constant
Question: A mass $m=50 \mathrm{~g}$ is dropped on a vertical spring of spring constant $500 \mathrm{~N} / \mathrm{m}$ from a height $\mathrm{h}=10 \mathrm{~cm}$ as shown in fig. The mass sticks to the spring ans executes simple harmonic oscillation after that. A concave mirror of focal length $12 \mathrm{~cm}$ facing the mass is fixed with its principal axis coinciding with the line of motion of the mass, its pole being at a distance of $30 \mathrm{~cm}$ from the free end of the spring. Find the...
Read More →A gun of mass M fires a bullet of mass m with
Question: A gun of mass $M$ fires a bullet of mass $m$ with a horizontal speed V. The gun is fitted with a concave mirror of focal length $f$ facing towards the receding bullet. Find the speed of separation of the bullet and the image just after the gun was fired. Solution:...
Read More →A small block of mass m and a concave mirror of radius
Question: A small block of mass $\mathrm{m}$ and a concave mirror of radius $\mathrm{R}$ fitted with a stand lie on a smooth horizontal table with a separation d between them. The mirror together with its stand has a mass m. The block is pushed at $\mathrm{t}=0$ towards the mirror so that it starts moving towards the mirror at a constant speed $\mathrm{V}$ and collides with it. The collision is perfectly elastic. Find the velocity of the image (a) at a time $td / V,(b)$ at a time $td / V$. Solut...
Read More →A particle is moving at a constant speed
Question: A particle is moving at a constant speed $\mathrm{V}$ from a large distance towards a concave mirror of radius $\mathrm{R}$ along its principal axis. Find the speed of the image formed by the mirror as a function of the distance $x$ of the particle from the mirror. Solution:...
Read More →A ball is kept at a height h above the surface of a heavy
Question: A ball is kept at a height $h$ above the surface of a heavy transparent sphere made of a material of refractive index $\mu$. The radius of the sphere is $\mathrm{R}$. At $\mathrm{t}=0$, the ball is dropped to fall normally on the sphere. Find the speed of the image formed as a function of time for $t\sqrt{\frac{2 h}{g}}$. Consider only the image by a single refraction. Solution:...
Read More →Two convex lenses, each of focal length
Question: Two convex lenses, each of focal length $10 \mathrm{~cm}$, are placed at a separation of $15 \mathrm{~cm}$ with their principal axes coinciding (a) show that a light beam coming parallel to the principal axis diverges as it comes out of the lens system. (b) Find the location of the virtual image formed by the lens system of an object placed far away. (c) Find the focal length of the equivalent lens. (note that the sign of the focal length is positive although the lens system actually d...
Read More →A point object is placed at a distance of
Question: A point object is placed at a distance of $15 \mathrm{~cm}$ from a convex lens. The image is formed on the other side at a distance of $30 \mathrm{~cm}$ from the lens. When a concave lens is placed in contact with the convex lens, the image shifts away further by $30 \mathrm{~cm}$. Calculate the focal lengths of the two lenses. Solution:...
Read More →A 5 mm high pin is placed at a distance of 15cm
Question: A $5 \mathrm{~mm}$ high pin is placed at a distance of $15 \mathrm{~cm}$ from a convex lens focal length $10 \mathrm{~cm}$. A second lens of focal length $5 \mathrm{~cm}$ is placed $40 \mathrm{~cm}$ from the first lens and $55 \mathrm{~cm}$ from the pin. Find (a) the position of the final image, (b) its nature and (c) its size. Solution:...
Read More →A diverging lens of focal length 20 cm and a converging lens
Question: A diverging lens of focal length $20 \mathrm{~cm}$ and a converging lens of focal length $30 \mathrm{~cm}$ are placed $15 \mathrm{~cm}$ apart with their principal axes coinciding. Where should an object be placed on the principal axis so that its image is formed at infinity? Solution:...
Read More →A convex lens of focal length 20cm
Question: A convex lens of focal length $20 \mathrm{~cm}$ and a concave lens of focal length $10 \mathrm{~cm}$ are placed $10 \mathrm{~cm}$ apart with their principal axis coinciding. A beam of light travelling parallel to the principal axis and having a beam diameter $5 \mathrm{~mm}$, is incident on the combination. Show that the emergent beam is parallel to the incident one. Find the beam diameter of the emergent beam. Solution:...
Read More →A point object is placed on the principal axis of
Question: A point object is placed on the principal axis of a convex lens $(f=15 \mathrm{~cm})$ at a distance of $30 \mathrm{~cm}$ from it. A glass Plate $(\mu=1.50)$ of thickness $1 \mathrm{~cm}$ is placed on the other side of the lens perpendicular to the axis, Locate the image of the point object. Solution:...
Read More →A converging lens of focal length
Question: A converging lens of focal length $15 \mathrm{~cm}$ and a converging mirror of focal length $10 \mathrm{~cm}$ are placed $50 \mathrm{~cm}$ apart. If a pin of length $2 \mathrm{~cm}$ is placed $30 \mathrm{~cm}$ from the lens farther away from the mirror, where will the final image form and what will be the size of the final image? Solution:...
Read More →Consider the situation describe in the previous problem.
Question: Consider the situation describe in the previous problem. Where should a point source be placed on the principal axis so that the two image from at the same place? Solution:...
Read More →A converging lens focal length 15cm and a converging mirror
Question: A converging lens focal length $15 \mathrm{~cm}$ and a converging mirror of focal length $10 \mathrm{~cm}$ are placed $50 \mathrm{~cm}$ apart with common principal axis. A point source is placed in between the lens and the mirror at a distance of $40 \mathrm{~cm}$ from the lens. Find the location of the images formed. Solution:...
Read More →A converging lens and a diverging mirror are placed
Question: A converging lens and a diverging mirror are placed at a separation of $15 \mathrm{~cm}$. The focal length of the lens is $25 \mathrm{~cm}$ and that of the mirror is $40 \mathrm{~cm}$. Where should a point source be placed between the lens and the mirror so that the light, after getting reflected by the mirror and then getting transmitted by the lens, comes out parallel to the principal axis? Solution:...
Read More →A converging lens of focal length
Question: A converging lens of focal length $12 \mathrm{~cm}$ and a diverging mirror of focal length $7.5 \mathrm{~cm}$ are placed $5 \mathrm{~cm}$ apart with their principal axis coinciding. Where should an object be placed so that its image falls on itself? Solution:...
Read More →A diverging lens of focal length
Question: A diverging lens of focal length $20 \mathrm{~cm}$ and a converging mirror of focal length $10 \mathrm{~cm}$ are placed coaxially at a separation of $5 \mathrm{~cm}$. Where should an object be placed so that a real image is formed at the object itself? Solution:...
Read More →A 5.0 diopter lens forms a virtual image which is 4 times
Question: A $5.0$ diopter lens forms a virtual image which is 4 times the object placed perpendicular on the principal axis of the lens. Find the distance of the object from the lens. Solution:...
Read More →The diameter of the sun is
Question: The diameter of the sun is $1.4 \times 10^{9} \mathrm{~m}$ and its distance from the earth is $1.5 \times 10^{11} \mathrm{~m}$. Find the radius of the image of the sun formed by a lens of focal length $20 \mathrm{~cm}$. Solution:...
Read More →A pin of length 2cm lies along the principal axis of
Question: A pin of length $2 \mathrm{~cm}$ lies along the principal axis of a converging lens, te center being at a distance of $11 \mathrm{~cm}$ from the lens. The focal length of the lens is $6 \mathrm{~cm}$. Find the size of the image. Solution:...
Read More →A convex lens produces a double size real image
Question: A convex lens produces a double size real image when an object is placed at a distance of $18 \mathrm{~cm}$ from it. Where should the object be placed to produce a triple size real image? Solution:...
Read More →A pin of length 2cm is placed perpendicular to the principal axis
Question: A pin of length $2 \mathrm{~cm}$ is placed perpendicular to the principal axis of a converging lens. An inverted image of size $1 \mathrm{~cm}$ is formed at a distance of $40 \mathrm{~cm}$ from the pin. Find the focal length of the lens and its distance from the pin. Solution:...
Read More →An extended object is placed at a distance of
Question: An extended object is placed at a distance of $5.0 \mathrm{~cm}$ from a convex lens of focal length $8 \mathrm{~cm}$ (a) dram a ray diagram (to the scale) to locate the image and from this, measure the distance of the image from the lens. (b) Find the position of the image from the lens formula and see how close the drawing is to the correct result. Solution:...
Read More →A particle executes a simple harmonic motion of
Question: A particle executes a simple harmonic motion of amplitude $1.0 \mathrm{~cm}$ along the principal axis of a convex lens of focal length $12 \mathrm{~cm}$. The mean position of oscillation is at $20 \mathrm{~cm}$. from the lens. Find the amplitude of oscillation of the image of the particle. Solution:...
Read More →A slide projector has to project a
Question: A slide projector has to project a $35 \mathrm{~mm}$ slide $(35 \mathrm{~mm} \times 23 \mathrm{~mm})$ on a $2 \mathrm{~m} \times 2 \mathrm{~m}$ screen at a distance of $10 \mathrm{~m}$ from the lens. What should be the focal length of the lens in the project? Solution:...
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