Advertisements
Advertisements
प्रश्न
A small candle, 2.5 cm in size is placed at 27 cm in front of a concave mirror of radius of curvature 36 cm. At what distance from the mirror should a screen be placed in order to obtain a sharp image? Describe the nature and size of the image. If the candle is moved closer to the mirror, how would the screen have to be moved?
Advertisements
उत्तर
Size of the candle, h = 2.5 cm
Image size = h'
Object distance, u = −27 cm
Radius of curvature of the concave mirror, R = −36 cm
Focal length of the concave mirror, f = `"R"/2 = (-36)/2` = −18 cm
Image distance = v
The image distance can be obtained using the mirror formula:
`1/"u" + 1/"v" = 1/"f"`
`1/"v" = 1/"f" - 1/"u"`
= `1/-18 - 1/-27`
= `(-3 + 2)/54`
= `-1/54`
∴ v = −54 cm
Therefore, the screen should be placed 54 cm away from the mirror to obtain a sharp image.
The magnification of the image is given as:
`"m" = "h'"/"h" = - "v"/"u"`
∴ h' = `-"v"/"u" xx "h"`
= `-(-54)/(-27) xx 2.5`
= −5 cm
The height of the candle’s image is 5 cm. The negative sign indicates that the image is inverted and real.
If the candle is moved closer to the mirror, then the screen will have to be moved away from the mirror in order to obtain the image.
संबंधित प्रश्न
If an object far away from a convex mirror moves towards the mirror, the image also moves. Does it move faster, slower or at the same speed as compared to the object?
In image formation from spherical mirrors, only paraxial rays are considered because they
A narrow pencil of parallel light is incident normally on a solid transparent sphere of radius r. What should be the refractive index is the pencil is to be focussed (a) at the surface of the sphere, (b) at the centre of the sphere.
A converging lens of focal length 12 cm and a diverging mirror of focal length 7.5 cm are placed 5.0 cm apart with their principal axes coinciding. Where should an object be placed so that its image falls on itself?
A converging lens of focal length 40 cm is kept in contact with a diverging lens of focal length 30 cm. Find the focal length of the combination .
Two thin lenses having optical powers of -10D and+ 6D are placed in contact with each other. The focal length of the combination is:
State how the focal length of a glass lens (Refractive Index 1.5) changes when it is completely immersed in:
(i) Water (Refractive Index 1.33)
(ii) A liquid (Refractive Index 1.65)
According to Cartesian sign convention, all distances are measured from the _______.
According to the mirror equation, ______.
The focal length of a convex lens made of glass of refractive index (1.5) is 20 cm.
What will be its new focal length when placed in a medium of refractive index 1.25?
Is focal length positive or negative? What does it signify?
The radius of curvature of the curved surface of a plano-convex lens is 20 cm. If the refractive index of the material of the lens be 1.5, it will ______.
A car is moving with at a constant speed of 60 km h–1 on a straight road. Looking at the rear view mirror, the driver finds that the car following him is at a distance of 100 m and is approaching with a speed of 5 km h–1. In order to keep track of the car in the rear, the driver begins to glance alternatively at the rear and side mirror of his car after every 2 s till the other car overtakes. If the two cars were maintaining their speeds, which of the following statement (s) is/are correct?
A spherical mirror is obtained as shown in the figure from a hollow glass sphere. if an object is positioned in front of the mirror, what will be the nature and magnification of the image of the object? (Figure drawn as schematic and not to scale)
Why does a car driver use a convex mirror as a rear-view mirror?
A lens of focal length f is divided into two equal parts and then these parts are put in a combination as shown in the figure below.
- What is the focal length of L1?
- What is the focal length of the final combination?
