To find the magnification of the object placed in front of a convex mirror, we can use the formula for magnification \( m \) in the context of mirrors:
\(m = \frac{h'}{h} = \frac{-v}{u}\)
where:
- \( h' \) is the height of the image.
- \( h \) is the height of the object.
- \( v \) is the image distance.
- \( u \) is the object distance (given as -10 cm since the object is on the left side of the mirror, according to the sign convention for mirrors).
For a convex mirror, the focal length \( f \) is positive. Given: \( f = 15 \, \text{cm} \) and \( u = -10 \, \text{cm} \).
Using the mirror formula,
\(\frac{1}{f} = \frac{1}{v} + \frac{1}{u}\)
Substitute the values:
\(\frac{1}{15} = \frac{1}{v} + \frac{1}{-10}\)
Rearrange to solve for \( \frac{1}{v} \):
\(\frac{1}{v} = \frac{1}{15} + \frac{1}{10}\)
Calculate the right-hand side:
\(\frac{1}{v} = \frac{2}{30} + \frac{3}{30} = \frac{5}{30} = \frac{1}{6}\)
Therefore,
\(v = 6 \, \text{cm}\)
Now calculate the magnification \( m \):
\(m = \frac{-v}{u} = \frac{-6}{-10} = +0.6\)
Hence, the magnification of the object by the convex mirror is +0.6.
Let's validate the options given in the question:
- +0.3 - Incorrect. This does not match the computed magnification.
- +0.6 - Correct. This matches the computed magnification.
- -0.3 - Incorrect. The sign is wrong and does not match the computed magnification.
- -0.6 - Incorrect. The sign is wrong and does not match the computed magnification.
Similar Questions
- If an object is placed between infinity and the pole (P) in front of a convex mirror, what type of image will be formed?
- A concave mirror produces three times magnified (enlarged) real image of object placed at 10 cm in front of it. Which option describes the image correctly?
- Which of the following mirrors is used by doctors to focus a parallel beam of light on the patient's organs like teeth for the examination?
- The radius of curvature of a spherical mirror is 20 cm. Its focal length is:
- The nature of the image formed by a concave mirror if the magnification produced by the mirror is +3 is:
Important Questions from Mirrors and Images
Which one of the following telescopes contains only mirrors?
The correct relation between the radius of curvature R and focal length f of a spherical mirror is
Spherical mirror formula relating an object distance ‘u’, image distance ‘v’ and focal length of mirror ‘f’ may be applied to a plane mirror when
The image of an object formed by a plane mirror is
The image we see in plane mirror is
