 For a concave mirror producing a real, magnified image, the magnification (m) is given by m = −v/u, where v is the image distance and u is the object distance. Given that m = 3 and u = −10 cm (object distance is negative in mirror formula), we have 3 = − v/−10. Solving this, v=−30 cm. The image is located 30 cm in front of the mirror.

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## Introduction to Mirror Imaging

Understanding Image Formation: In optics, the way a mirror forms an image of an object depends on the type of mirror and the position of the object relative to the mirror. Concave mirrors, in particular, can produce various types of images based on these factors.

### Concave Mirror Characteristics

Properties of Concave Mirrors: A concave mirror is a spherical mirror that curves inward. It is capable of producing real, inverted images when the object is placed outside the focal point, and virtual, erect images when the object is within the focal point.

#### Given Scenario

Object Placement and Image Magnification: In the given scenario, an object is placed 10 cm in front of a concave mirror, and a real image that is three times magnified (enlarged) is produced. This indicates that the object is placed between the focal point and the center of curvature of the mirror.

##### Mirror Formula and Magnification

Applying Optical Principles: The relationship between object distance (u), image distance (v), and magnification (m) in mirror optics is given by m = −v/u. Here, magnification is positive for virtual images and negative for real images. Given
m = 3 and u = −10 cm (object distance is taken as negative in the mirror formula), we can find the image distance.

###### Calculation of Image Distance

Determining Image Location: Substituting the given values into the magnification formula, 3 = −v/−10, we can solve for v. This calculation gives v = −30 cm, indicating that the image is formed 30 cm in front of the mirror.

Image Position in Concave Mirror: Therefore, in this scenario, the concave mirror forms a real, magnified image 30 cm in front of it. This distance reflects the specific properties of the concave mirror and the object’s position relative to it.

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Questions of 10th Science Chapter 9 in Detail

 Define the principal focus of a concave mirror. The radius of curvature of a spherical mirror is 20 cm. What is its focal length? Name a mirror that can give an erect and enlarged image of an object. Why do we prefer a convex mirror as a rear-view mirror in vehicles? Find the focal length of a convex mirror whose radius of curvature is 32 cm. A concave mirror produces three times magnified (enlarged) real image of an object placed at 10 cm in front of it. Where is the image located? A ray of light travelling in air enters obliquely into water. Does the light ray bend towards the normal or away from the normal? Why? Light enters from air to glass having refractive index 1.50. What is the speed of light in the glass? Find out, from Table, the medium having highest optical density. Also find the medium with lowest optical density. You are given kerosene, turpentine and water. In which of these does the light travel fastest? The refractive index of diamond is 2.42. What is the meaning of this statement? Define 1 dioptre of power of a lens. A convex lens forms a real and inverted image of a needle at a distance of 50 cm from it. Where is the needle placed in front of the convex lens if the image is equal to the size of the object? Find the power of a concave lens of focal length 2 m. We wish to obtain an erect image of an object, using a concave mirror of focal length 15 cm. What should be the range of distance of the object from the mirror? Name the type of mirror used in the following situations. (a) Headlights of a car. (b) Side/rear-view mirror of a vehicle. (c) Solar furnace. One-half of a convex lens is covered with a black paper. Will this lens produce a complete image of the object? An object 5 cm in length is held 25 cm away from a converging lens of focal length 10 cm. What is the position, size and the nature of the image formed. A concave lens of focal length 15 cm forms an image 10 cm from the lens. How far is the object placed from the lens? An object is placed at a distance of 10 cm from a convex mirror of focal length 15 cm. Find the position and nature of the image. The magnification produced by a plane mirror is +1. What does this mean? An 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. An object of size 7.0 cm is placed at 27 cm in front of a concave mirror of focal length 18 cm. At what distance from the mirror should a screen be placed, so that a sharp focussed image can be obtained? Find the focal length of a lens of power – 2.0 D. What type of lens is this? A doctor has prescribed a corrective lens of power +1.5 D. Find the focal length of the lens. Is the prescribed lens diverging or converging?