A shop security mirror 5.0m from certain items displayed in the shop produces one-tenth magnification.
- What is the type of mirror?
- What is the radius of curvature of the mirror?
Download our app for free and get started
- It is a convex mirror, as it has a wide area of view.
- Given,
Magnification (m) = $\frac{1}{10}$
We have to find the position of the image (v), radius of curvature (R) and the focal length of the mirror (f).
Using the magnification formula, we get
$\text{m}=\frac{\text{-v}}{\text{u}}$
$\text{m}=\frac{\text{-v}}{-5}$
$\frac{1}{10}=\frac{\text{-v}}{-5}$
$\frac{1}{10}=\frac{\text{v}}{5}$
$\text{v}=0.5\text{m}$
Now, using the mirror formula, we get
$\frac{1}{\text{f}}=\frac{1}{\text{u}}+\frac{1}{\text{v}}$
$\frac{1}{\text{f}}=\frac{1}{-5}+\frac{1}{0.5}$
$\frac{1}{\text{f}}=\frac{1}{-5}+\frac{10}{5}$
$\frac{1}{\text{f}}=-\frac{1}{5}+\frac{10}{5}$
$\frac{1}{\text{f}}=-\frac{9}{5}$
$\text{f}=\frac{5}{9}$
$\text{R}=2\text{f}$
or $\text{R}=1.1$
Therefore, the radius of curvature of the mirror (R) is 1.1m.
Download our appand get started for free
Experience the future of education. Simply download our apps or reach out to us for more information. Let's shape the future of learning together!No signup needed.*
Similar Questions
- 1View SolutionCalculate the image distance for an object of height 12mm at a distance of 0.20m from a concave lens of focal length 0.30 m, and state the nature and size of the image.
- 2View SolutionTwo lenses A and B have power of (i) + 2 D and (ii) -4D respectively. What is the nature and focal length of each lens?
- 3View SolutionAn object 5.0 cm in length is placed at a distance of 20 cm in front of a convex mirror of radius of curvature 30 cm. Find the position of the image, its nature and size.
- 4View SolutionAn object of size 7.0cm is placed at 27cm in front of a concave mirror of focal length 18cm. At what distance from the mirror should a screen be placed so that a sharp focussed image can be obtained? Find the size and nature of image.
[Hint. Find the value of image distance (v) first. The screen should be placed from the mirror at a distance equal to image distance.] - 5View SolutionState the laws of refraction of light. Explain the term ‘absolute refractive index of a medium’ and write an expression to relate it with the speed of light in vacuum.
- 6View SolutionA man standing in front of a special mirror finds his image having a very small head, a fat body and legs of normal size. What is the shape of:
- Top part of the mirror?
- Middle part of the mirror?
- Bottom part of the mirror?
- 7View SolutionAn object is placed at a distance of 100cm from each of the above lenses A and Calculate:
- Image distance, and
- Magnification, in each of the two cases.
- 8View SolutionA spherical mirror produces an image of magnification -1 on a screen placed at a distance of 50cm from the mirror.
- Write the type of mirror.
- find the distance of the image from the object.
- What is the focal length of the mirror?
- Draw the ray diagram to show the image formation in this case.
- 9View SolutionName the type of mirror used in the following situations.
- Headlights of a car.
- Side/rear-view mirror of a vehicle.
- Solar furnace.
- 10View SolutionName the type of mirror used:
- By dentists.
- In solar furnaces. Give two reasons why such mirrors are used in each case.