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Numerical Problems From Optics

  1. When an object of height 4cm is placed at 40cm from a mirror the mirror forms the image on the object itself. If the height of the image is equal to the height of the object. Find out the focal length of the mirror and identify the mirror.
  2. A convergent beam of light passes through a diverging lens of focal length 0.2m and comes to focus at distance 0.3m behind the lens.Find the position of the point at which the beam would converge in the absence of lens?

A problem from Optics

A convergent beam of light passes through a diverging lens of focal length 0.2m and comes to focus at distance 0.3m behind the lens.Find the position of the point at which the beam would converge in the absence of lens?

Spherical Mirror Problem

A rear view mirror used in a bus has a radius of curvature 3.5 m. If the driver of the bus locates a car at 10.0m behind the bus, find the position, nature and size of the image of the car.

Ans:

f = r/2=-1.75 m

u=-10m

v=?


Numerical Problems from Light

Madhu sent us the following problems from “Light”. Visitors can attempt to solve the problems by quoting the question number.

Most of the questions below are based on mirror formula and lens formula.

 

Mirror Formula

\LARGE\frac{1}{u}+\frac{1}{v}=\frac{1}{f}

 

Lens Formula  

\Large \frac{1}{v}-\frac{1}{u}=\frac{1}{f}

Now try solving these questions/problems. If in doubt or not able to solve the problems, just post your problems as comments and we are here to help you out.

  1. A rear view mirror used in a bus has a radius of curvature 3.5 m. If the driver of the bus locates a car at 10.0m behind the bus, find the position, nature and size of the image of the car.
  2. An object 4cm high is placed at a distance of 6 cm in front of a concave mirror of focal length 12 cm. Find the position, nature and size of the image formed.
  3. An object 50 cm tall is placed on the principal axis of a convex lens. Its 20cm tall image is formed on the screen placed at a distance of 10 cm from the lens. Calculate the focal length of the lens.
  4.  A concave lens has focal length 20cm. At what distance from the lens a 5 cm tall object should be placed so that it forms an image at 15 cm from the lens? Also calculate the size of the image formed.
  5. An object 2.0 cm in size is placed 20.0 cm in front of a concave mirror of focal length 10.0 cm. Find the distance from the mirror at which a screen should be placed in order to obtain a sharp image. What will be the size and nature of the image formed?
  6. A convex lens has a focal length of 30 cm. Calculate at what distance should the object be placed from the lens so that it forms an image at 60 cm on the other side of the lens. Find the magnification produced by the lens in this case.
  7. The radius of curvature of a convex mirror used on a moving automobile is 2.0 m. A truck is coming behind it at a constant distance of 3.5 m. Calculate (i) the position and (ii) the size of the image relative to the size of the truck. What will be the nature of the image?
  8. Find the position of an object which when placed in front of a concave mirror of focal length 20 cm produces a virtual image, which is twice the size of the object.
  9. A concave mirror of focal length 20 cm forms a real, inverted image of same size as that of the object. Where is the object placed with respect to the mirror? Draw a diagram to show the image formation?
  10. The radius of curvature of a concave mirror is -46cm.What is its focal length?
  11. A convex mirror used on an automobile has radius of curvature of 2 m .If a car is located at 4 m from the mirror, find the position nature and size of the image
  12. An object is kept in front of a concave mirror of focal length 20cm.The image formed is three times the size of the object. Calculate the two possible distances of the object from the mirror.
  13. An object 4cm high is placed 15cm away from a concave lens of focal length 10cm. Draw a ray diagram and find the position, size and nature of the image formed.
  14. An object 0.4m high is placed at a distance of 0.8m from a concave mirror of radius curvature 0.4m. Find the position, nature and size of the image formed?
  15. Two thin converging lenses of focal length 15cm and 30cm are held in contact with each other. Calculate the power and focal length of combination.
  16. You are required to obtain an erect image of an object placed in front of a concave mirror of focal length 15cm.What should be the approximate distance of the object from the pole of the mirror? What is the nature of the image? Is the image larger of smaller in size than the object? Draw a ray diagram to show the formation of image.
  17. An object of size 5cm is placed at a distance of 25cm from the pole of a concave mirror of radius of curvature 30cm.Calculate the distance and size of the image so formed. What will be the nature of the image?
  18. An object of size 3cm is placed at a distance of 15cm from a convex lens of focal length 10cm.Calculate the distance and size of the image so formed. What will be the nature of the image?
  19. A 1cm high image is obtained on a screen a t a distance of 20cm from a convex lens of focal length 10cm.What is the size the object?
  20. The radius of curvature of a convex mirror is used on a moving automobile is 2.0 m. A truck is coming behind it at a constant distance of 3.5 m. Calculate (1) the position, and (2) the size of image relative to the size of the truck. What will be the nature of the image?
  21. A concave lens of focal length 15 cm forms an image 10 cm from the lens? How far is the object placed from the lens?
  22. An object of size 3 cm is placed at a distance of 15 cm from a convex lens of focal length 10 cm. Calculate the distance and the size of the image so formed. What will be the nature of image formed?
  23. A converging mirror forms a real image of height 6 cm of an object of height 2 cm placed 20 cm away from the mirror. Find the image distance and the focal length of the mirror.
  24. An object is placed at a distance of 10cm from a convex mirror of focal length 15 cm. Find the position and nature of the image
  25. An object 5 cm in length is held 25 cm away from a converging lens of focal length 10cm. Draw the ray diagram and find the position, size and nature of the image formed.
  26. An object is placed at 10cm in front of a concave mirror of focal length 15cm. Find the position, nature and size of the image

Motion in a vertical circle and conservation of energy

A stone  tied to a string of length l is whirled around a vertical circle with the other end of the string at the centre. At a certain instant of time the stone is at the lowest position and has a speed u. What is the magnitude of change in its velocity as it reaches a position where the string is horizontal?

Answer:

Let’s assume that the potential energy at the lowest position be zero. So, when the string is horizontal, the stone has risen by a vertical height l, the length of the string which is also the radius of the vertical circle.

If v is the magnitude of velocity at the horizontal position, then according to the law of conservation of energy,

KE+PE at the lowest position = KE+PE at the horizontal position

\frac{1}{2}mu^{2}=\frac{1}{2}mv^{2}+mgl

From the equation above, v-u can be calculated.

v=\sqrt{u^{2}-2gl}

 

The following links will help you for deeper understanding and you can browse through some solved problems from the topic too.

Relative position of a helicopter

If a helicopter takes off from a point on earth.(at certain altitude) and its still at that point in air.After certain time interval the observer whose position was same as that of helicopter’s take off point will see the helicopter right above him.
The question arises is that how it is possible if earth is rotating hence the observer is also, but the helicopter is in air.How is it possible?
Please explain.
Thanks…

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Big Bang Theory

‘BIG BANG’ theory is well known to all . If it actually happened, Then I thought a question about this, like as what is the actual position of our earth in the previous time of ‘BIG BANG’?? When the whole earth is like a point. … Arkajyoti asked

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