When an object of height 1cm is kept at a distance 4cm from a concave mirror,its erect image of height 1.5cm is formed at a distance 6cm behind the mirror.find the focallength of mirror,by drawing
To find the focal length of a concave mirror using the given information, we can make use of the mirror formula:
1/f = 1/v - 1/u,
where:
- "f" is the focal length of the mirror,
- "v" is the image distance (distance between the mirror and the image),
- "u" is the object distance (distance between the mirror and the object).
In this case, the object height (h = 1cm) and the image height (h' = 1.5cm) are given. However, we don't need to use these measurements to determine the focal length.
1. Start by drawing a rough diagram where the concave mirror is represented by a smooth curved line.
2. Mark a point on the principal axis (the horizontal line passing through the mirror's center) to represent the mirror's vertex.
3. Place the object at a distance of 4cm in front of the mirror along the principal axis. This will be the object distance (u).
4. Draw a straight line from the top of the object (on the principal axis) which passes through the vertex of the mirror.
5. From the intersection point of the line in step 4 with the principal axis, draw another line going to the left, behind the mirror. This represents the path of the reflected light rays.
6. Locate the image of the object by extending the reflected rays back to meet. Mark the point on the principal axis where the reflected rays meet as the image distance (v).
7. Measure the object distance (u), which is 4cm, and the image distance (v), which is 6cm.
8. Substitute the values for u and v into the mirror formula: 1/f = 1/v - 1/u.
1/f = 1/6 - 1/4.
9. Simplify the equation:
1/f = (4 - 6)/(6 * 4) = -2/24.
1/f = -1/12.
10. Invert both sides of the equation:
f = -12/1.
11. Solve for f:
f = -12cm.
Therefore, the focal length of the concave mirror is -12cm. Note that the negative sign indicates that the mirror is concave.
To find the focal length of the concave mirror, we can use the mirror formula:
1/f = 1/v - 1/u
Where:
f = focal length of the concave mirror
v = image distance from the mirror
u = object distance from the mirror
Given:
Height of object (h1) = 1 cm
Distance of object from the mirror (u) = 4 cm
Height of image (h2) = 1.5 cm
Distance of image from the mirror (v) = -6 cm (since the image is formed behind the mirror)
Step 1: Convert the distances to positive values in the formula
Since the image distance is negative, we treat it as a positive value for calculation purposes:
u = 4 cm
v = -(-6 cm) = 6 cm
Step 2: Substitute the values into the formula
1/f = 1/6 - 1/4
Step 3: Solve the equation
1/f = (4 - 6) / (4 * 6)
1/f = -2 / 24
1/f = -1/12
To get the focal length, we can take the reciprocal of both sides:
f = -12 cm
Therefore, the focal length of the concave mirror is -12 cm.