 The power of a lens (P) is related to its focal length (f) by the formula P = 1/f, where f is in meters. For a lens with a power of +1.5 D, the focal length is f = 1/1.5 meters, which equals approximately 0.67 meters or 67 cm. The positive sign of the power indicates that the lens is a converging lens, typically used to correct farsightedness.

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## Introduction to Lens Power and Focal Length

Understanding Lens Power: The power of a lens, measured in dioptres (D), is a key optical property that indicates its ability to converge or diverge light. It is directly related to the focal length of the lens, providing insight into its function.

### Prescription Details

Lens Power Prescribed by Doctor: A doctor has prescribed a corrective lens with a power of +1.5 dioptres. The positive value of the power suggests a specific type of lens, which can be identified by calculating its focal length.

#### Calculating Focal Length

Using the Power Formula: The relationship between the power (P) of a lens and its focal length (f) is given by P = 1/f, where f is expressed in meters. To find the focal length of a lens with a power of +1.5 D, we rearrange this formula to f = 1/P.

##### Determining the Focal Length

Focal Length Calculation: Substituting the power value into the formula, f = 1/1.5, we find that the focal length is approximately 0.67 meters or 67 cm. This value is crucial in identifying the type of lens.

###### Identifying the Type of Lens

Nature of the Lens: The positive focal length indicates that the lens is a converging lens. Converging lenses, such as convex lenses, are characterized by their ability to bring light rays together.

Characteristics of the Prescribed Lens: Therefore, a lens with a power of +1.5 dioptres has a focal length of approximately 67 cm and is a converging lens. This type of lens is commonly used in corrective eyewear to address issues like farsightedness, where converging lenses help focus light onto the retina.

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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?