 To find the object distance for a concave lens, we use 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. For a concave lens, f is -15 cm and v is -10 cm (since it forms a virtual image). Rearranging and solving, 1/−15 = 1/−10 − 1/u, we find u ≈ − 30 cm. The object is placed 30 cm from the lens.

Let’s discuss in detail

## Introduction to Lens Formula Application

Understanding Lens Mechanics: The lens formula is a fundamental tool in optics, used to determine the relationship between the object distance, image distance, and focal length of a lens. It is particularly useful in calculating the position of an object or an image formed by lenses.

### Concave Lens Characteristics

Nature of a Concave Lens: A concave lens is a diverging lens, meaning it spreads out light rays that pass through it. The focal length of a concave lens is considered negative, as it diverges light rather than converging it.

#### Given Scenario

Image Formation by a Concave Lens: In the provided scenario, a concave lens with a focal length of 15 cm forms an image 10 cm from the lens. Since concave lenses always form virtual images on the same side as the object, the image distance is also negative.

##### Applying the Lens Formula

Lens Formula Calculation: The lens formula is 1/f = 1/v − 1/u, where f is the focal length, v is the image distance, and u is the object distance. For a concave lens with f = −15 cm and v = −10 cm, this formula can be used to find u.

###### Calculating Object Distance

Solving for Object Position: Substituting the given values into the lens formula, we get 1/−15 = 1/−10 − 1/u. Solving for u gives us the object distance. The calculation reveals that u is approximately -30 cm.

Result Interpretation: The negative sign indicates that the object is located on the same side of the lens as the light source. Therefore, in this scenario, the object is placed 30 cm from the concave lens. This demonstrates how the lens formula is essential in determining the positions of objects and images in lens systems.

Discuss this question in detail or visit to Class 10 Science Chapter 9 for all questions.
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?