 When a convex lens forms a real, inverted image equal in size to the object, the object is placed at 2F (twice the focal length). Since the image distance (v) is 50 cm, the object distance (u) is also 50 cm. The lens formula 1/f = 1/v + 1/u gives 1/f = 1/50 + 1/50, so f = 25 cm. The power (P) is P = 1/f in meters, so P = 1/0.25 = 4 dioptres. The needle is 50 cm from the lens, and the lens power is 4 dioptres.

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## Introduction to Image Formation by Lenses

Optical Principles of Lenses: In optics, lenses are used to form images of objects by refracting light. The nature of the image formed – whether real or virtual, inverted or erect – depends on the object’s distance from the lens and the lens’s focal length.

### Convex Lens Characteristics

Converging Properties: A convex lens is a converging lens, meaning it brings light rays together. It can form real, inverted images of objects placed at various distances from the lens.

#### Given Scenario

Equal Size Image Formation: In the given scenario, a convex lens forms a real and inverted image of a needle, which is equal in size to the needle itself. This specific condition occurs when the object is placed at twice the focal length (2F) of the lens.

##### Determining Object Distance

Application of Lens Formula: Using the lens formula 1/f = 1/v + 1/u, where f is the focal length, v is the image distance, and u is the object distance, we can determine the position of the needle. Given that the image distance v is 50 cm, and knowing that u=v in this case, we find that the object is also 50 cm from the lens.

###### Calculating the Lens Power

Finding Focal Length and Power: The focal length f can be calculated using the same lens formula. Substituting v = 50 cm and u = 50 cm, we find f = 25 cm. The power P of a lens is given by P = 1/ f in meters, which in this case is 1/0.25 = = 4 dioptres.

Summary of Findings: Therefore, in this scenario, the needle is placed 50 cm in front of the convex lens, and the power of the lens is 4 dioptres. This setup allows for the formation of a real, inverted image of the needle that is equal in size to the needle itself.

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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?