A pin 2 cm long is placed 12 cm away from a convex lens at right angles to the principal axis. If the focal length of the lens is 20 cm, by scale drawing and lens formula find the nature , size and position of image.
52.5
To find the nature, size, and position of the image formed by a convex lens, we can use the lens formula:
1/f = 1/v - 1/u
Where:
- f is the focal length of the lens,
- v is the distance of the image from the lens,
- u is the distance of the object from the lens.
In this case, the object (pin) is placed 12 cm away from the lens, and the focal length of the lens is 20 cm.
First, let's find the location of the image using the lens formula. Rearranging the formula, we have:
1/v = 1/f + 1/u
Substituting the values, we get:
1/v = 1/20 + 1/12
Now, calculate the values:
1/v = (12 + 20) / (12 * 20)
1/v = 32 / 240
1/v = 1/7.5
Taking the reciprocal of both sides, we get:
v = 7.5 cm
So, the image is formed at a distance of 7.5 cm from the lens.
Next, let's find the magnification (size) of the image. The magnification, M, is given by the formula:
M = -v/u
Substituting the values, we get:
M = -7.5 / 12
M = -0.625
Since the magnification is negative, it indicates that the image formed is inverted.
Finally, let's determine the nature of the image. For a convex lens, when the object is placed beyond the focal point, the image formed is real and inverted. So, in this case, the image formed is real, inverted, and smaller in size compared to the object.
To create a scale drawing to represent this, you can use a ruler and paper. Choose a suitable scale (e.g., 1 cm = 5 cm) and draw the principal axis. Place a dot on the principal axis to represent the object at 12 cm from the lens. Then, using the calculated values, draw an arrow or dot to represent the image at a distance of 7.5 cm from the lens, below the principal axis.
Remember, a scale drawing is an approximation, so the proportions may not be exact, but it should represent the general shape, position, and orientation of the image.