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प्रश्न
A student places a 8.0 cm tall object perpendicular to the principal axis of a convex lens of focal length 20 cm. The distance of the object from the lens is 30 cm. He obtains a sharp image of the object on a screen placed on the other side of the lens. What will be the nature (inverted, erect, magnified, diminished) of the image he obtains on a screen? Draw ray diagram to justify your answer.
उत्तर
Focal length of the lens, f = 20 cm
Object distance, u = −30 cm
According to the lens formula,
\[\frac{1}{v} - \frac{1}{u} = \frac{1}{f}\]
\[ \Rightarrow \frac{1}{v} = \frac{1}{f} + \frac{1}{u}\]
\[ \Rightarrow \frac{1}{v} = \frac{1}{20} - \frac{1}{30}\]
\[ \Rightarrow v = 60 cm\]
\[\text{ Magnification }, m = \frac{v}{u}\]
\[ \Rightarrow m = \frac{60}{\left( - 30 \right)} = - 2\]
Hence, the image formed is real, inverted and magnified.
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संबंधित प्रश्न
Analyse the following observation table showing variation of image-distance (v) with object-distance (u) in case of a convex lens and answer the questions that follow without doing any calculations :
| S. No. | Object-Distance u (cm) |
Image-Distance v (cm) |
| 1 | –100 | +25 |
| 2 | –60 | +30 |
| 3 | –40 | +40 |
| 4 | –30 | +60 |
| 5 | –25 | +100 |
| 6 | –15 | +120 |
(a) What is the focal length of the convex lens? Give reason to justify your answer.
(b) Write the serial number of the observation which is not correct. On what basis have you arrived at this conclusion?
(c) Select an appropriate scale and draw a ray diagram for the observation at S.No. 2. Also find the approximate value of magnification.
A beam of light travelling in a rectangular glass slab emerges into air. Draw a ray-diagram indicating the change in its path.
f the image formed by a convex lens is of the same size as that of the object, what is the position of the image with respect to the lens?
Where should an object be placed in front of a convex lens so as to obtain its virtual, erect and magnified image?
An object is placed at a distance equal to 2f in front of a convex lens. Draw a labelled ray diagram to show the formation of image. State two characteristics of the image formed.
A convex lens produces an inverted image magnified three times of an object placed at a distance of 15 cm from it. Calculate focal length of the lens.
An object 2 cm tall is placed on the axis of a convex lens of focal length 5 cm at a distance of 10 m from the optical centre of the lens. Find the nature, position and size of the image formed. Which case of image formation by convex lenses is illustrated by this example?
Find the nature, position and magnification of the images formed by a convex lens of focal length 0.20 m if the object is placed at a distance of:
0.15 m
In the following cases, where must an object be placed in front of a convex lens so that the image formed is of the same size as the object?
