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An object 3cm high is placed at a distance of 8cm from a concave mirror which produces a 4.5 high (a)what isthe focal length of the mirror.(b) what is position of image.(c)draw a raw diagram to show the formation of image.
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An object 3cm high is placed at a distance of 8cm from a concave mirro...
Focal Length of the Mirror
Given, object height (h1) = 3 cm, object distance (u) = -8 cm (as the object is in front of the mirror), and image height (h2) = 4.5 cm.
Using the mirror formula, 1/f = 1/u + 1/v, where f is the focal length and v is the image distance, we can calculate the focal length.
1/f = 1/-8 + 1/v
1/f = (v-8)/(-8v)
f = -8v/(v-8)
Now, we know that the magnification (m) of the image is given by h2/h1 = -v/u. Substituting the given values, we get:
m = 4.5/3 = -v/-8
v = 12 cm
Substituting this value of v in the formula for f, we get:
f = -96/4 = -24 cm
Therefore, the focal length of the mirror is -24 cm.
Position of Image
Using the mirror formula, 1/f = 1/u + 1/v, and substituting the values of f and u, we can calculate the image distance.
1/-24 = 1/-8 + 1/v
1/v = 1/-24 - 1/-8 = -1/24
v = -24 cm
Since the image distance is negative, the image is formed behind the mirror, and is therefore virtual.
Ray Diagram
To draw a ray diagram, we can use the following steps:
1. Draw a principal axis passing through the center of the mirror.
2. Mark the focal point (F) on the principal axis, which is at a distance of -24 cm from the mirror.
3. Draw a ray parallel to the principal axis, which after reflection passes through the focal point F.
4. Draw a ray passing through the focal point F, which after reflection becomes parallel to the principal axis.
5. From the top of the object, draw a ray towards the center of the mirror, which reflects back along the same path.
6. The point where the two reflected rays intersect is the position of the virtual image.
The final ray diagram will show a virtual image formed behind the mirror, which is upright and larger than the object.
Therefore, the focal length of the mirror is -24 cm, the position of the virtual image is -24 cm, and the ray diagram shows a virtual image formed behind the mirror, which is upright and larger than the object.
Given, object height (h1) = 3 cm, object distance (u) = -8 cm (as the object is in front of the mirror), and image height (h2) = 4.5 cm.
Using the mirror formula, 1/f = 1/u + 1/v, where f is the focal length and v is the image distance, we can calculate the focal length.
1/f = 1/-8 + 1/v
1/f = (v-8)/(-8v)
f = -8v/(v-8)
Now, we know that the magnification (m) of the image is given by h2/h1 = -v/u. Substituting the given values, we get:
m = 4.5/3 = -v/-8
v = 12 cm
Substituting this value of v in the formula for f, we get:
f = -96/4 = -24 cm
Therefore, the focal length of the mirror is -24 cm.
Position of Image
Using the mirror formula, 1/f = 1/u + 1/v, and substituting the values of f and u, we can calculate the image distance.
1/-24 = 1/-8 + 1/v
1/v = 1/-24 - 1/-8 = -1/24
v = -24 cm
Since the image distance is negative, the image is formed behind the mirror, and is therefore virtual.
Ray Diagram
To draw a ray diagram, we can use the following steps:
1. Draw a principal axis passing through the center of the mirror.
2. Mark the focal point (F) on the principal axis, which is at a distance of -24 cm from the mirror.
3. Draw a ray parallel to the principal axis, which after reflection passes through the focal point F.
4. Draw a ray passing through the focal point F, which after reflection becomes parallel to the principal axis.
5. From the top of the object, draw a ray towards the center of the mirror, which reflects back along the same path.
6. The point where the two reflected rays intersect is the position of the virtual image.
The final ray diagram will show a virtual image formed behind the mirror, which is upright and larger than the object.
Therefore, the focal length of the mirror is -24 cm, the position of the virtual image is -24 cm, and the ray diagram shows a virtual image formed behind the mirror, which is upright and larger than the object.
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An object 3cm high is placed at a distance of 8cm from a concave mirro...
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