All questions of Light for Class 10 Exam

Degrees with the mirror surface. The angle of reflection will also be 30 degrees, as the angle of incidence is equal to the angle of reflection for a plane mirror. This means that the light will bounce off the mirror at the same angle it came in at.

Explanation:

A concave mirror is a mirror with a curved reflective surface that bulges inward. It is also known as a converging mirror because it converges the light rays that fall on it. The linear magnification produced by a concave mirror can be positive or negative depending on the position of the object and the mirror.

Positive Linear Magnification:
When the object is placed between the focus and the pole of the concave mirror, a real and inverted image is formed. In this case, the linear magnification is positive. The image is magnified and located on the same side of the mirror as the object. This is because the light rays converge after reflection and form an enlarged image. The magnification can be calculated using the formula:

Magnification (m) = Height of Image (hᵢ) / Height of Object (hₒ)

Negative Linear Magnification:
When the object is placed beyond the focus of the concave mirror, a virtual and erect image is formed. In this case, the linear magnification is negative. The image is diminished and located on the opposite side of the mirror as the object. This is because the light rays diverge after reflection and form a smaller image. The magnification can still be calculated using the same formula as before, but the height of the image will be negative.

Convex Mirror:
A convex mirror is a mirror with a curved reflective surface that bulges outward. It is also known as a diverging mirror because it diverges the light rays that fall on it. The image formed by a convex mirror is always virtual, erect, and diminished in size. The linear magnification produced by a convex mirror is always positive, but it is less than 1. The magnification formula can still be used, but the height of the image will be smaller than the height of the object.

Therefore, option D is correct because the image formed by a convex mirror is always virtual and erect.

Torches, search lights, and headlights of vehicles

In torches, search lights, and headlights of vehicles, the bulb is placed very near to the focus of the reflector. This positioning ensures that the light rays from the bulb are reflected in a parallel manner, resulting in a focused and powerful beam of light.

Explanation:

1. Purpose of the reflector:
- The reflector in torches, search lights, and headlights of vehicles is used to control and direct the light emitted by the bulb.
- It is designed to reflect the light rays in a specific direction, increasing the intensity and reach of the light beam.

2. Reflectors and light rays:
- When light rays from the bulb fall on the reflector, they get reflected according to the laws of reflection.
- The reflector is usually a parabolic mirror, which has a special shape that helps in focusing the light.
- The parabolic shape of the reflector ensures that the light rays, after reflection, converge at a single point known as the focus.

3. Placing the bulb:
- Placing the bulb very near to the focus of the reflector helps in achieving a parallel beam of light.
- When the bulb is placed at the focus, the light rays emitted by the bulb are reflected by the reflector in such a way that they become parallel to each other.
- This parallel arrangement of light rays results in a powerful and focused beam of light.

4. Advantages of placing the bulb near the focus:
- The parallel arrangement of light rays increases the intensity of the light beam, making it brighter and more focused.
- It allows for long-range illumination, as the parallel rays travel in a straight line without much divergence.
- The focused beam helps in directing the light where it is needed, enhancing visibility and reducing light wastage.

Conclusion:

In torches, search lights, and headlights of vehicles, the bulb is placed very near to the focus of the reflector. This positioning ensures a parallel arrangement of light rays, resulting in a powerful and focused beam of light.

Explanation:

Convex lens with 4 dioptre power and a focal length of 0.25 m
- The power of a lens is given by the formula: Power (P) = 1 / focal length (f) in meters
- Given that the power of the convex lens is 4 dioptres, we can calculate the focal length using the formula: f = 1 / P
- Substituting the power value into the formula, we get: f = 1 / 4 = 0.25 m
- Therefore, a convex lens with a power of 4 dioptres will have a focal length of 0.25 m.
Therefore, option 'D' is the correct statement as it accurately describes a convex lens with 4 dioptre power and a focal length of 0.25 m.

Explanation:

To obtain a smaller inverted image using a convex lens, we need to place the object at a certain distance from the lens. The distance of the object from the lens can be determined using the lens formula:

1/f = 1/v - 1/u

Where:
- f is the focal length of the lens
- u is the distance of the object from the lens
- v is the distance of the image from the lens

In this case, the focal length of the lens is given as 50 cm.

Step 1: Identify the given information
- Focal length (f) = 50 cm

Step 2: Determine the required conditions for a smaller inverted image
To obtain a smaller inverted image, the image distance (v) should be smaller than the object distance (u). This can be achieved by placing the object beyond the focal point of the lens.

Step 3: Apply the lens formula to find the object distance
Substituting the given values into the lens formula:

1/50 = 1/v - 1/u

Simplifying the equation:

1/v = 1/50 + 1/u

To obtain a smaller inverted image, the value of 1/v should be smaller than 1/50. This implies that the value of 1/u should be greater than 1/50.

Step 4: Determine the object distance
To find the object distance that satisfies the condition, we can substitute different values of u and solve the equation.

Let's try option D: 1/120 = 1/50 + 1/u

Simplifying the equation:

1/u = 1/120 - 1/50
1/u = (5 - 12)/(120 * 50)
1/u = -7/6000

The value of 1/u is negative, indicating that the object is placed on the same side as the lens. This is the correct condition to obtain a smaller inverted image.

Therefore, the correct answer is option D: 120 cm, as it satisfies the conditions for obtaining a smaller inverted image.

Understanding the Types of Mirrors
To determine why a convex mirror is the correct answer for viewing a full-length image of a distant tall building, we must first understand the properties of different types of mirrors.
Concave Mirrors:
- Formation of Images: Concave mirrors can produce real and inverted images, as well as virtual and upright images depending on the object's distance from the mirror.
- Limitations: For distant objects, the image formed by concave mirrors can be minuscule and may not be practical for full-length viewing of a tall building.
Convex Mirrors:
- Wide Field of View: Convex mirrors diverge light rays, allowing them to capture a wider area. This characteristic is crucial when trying to view tall buildings from a distance.
- Image Characteristics: The images formed by convex mirrors are always virtual, erect, and reduced in size, making them suitable for observing large structures.
- Practical Use: Convex mirrors are commonly used in security and traffic applications for their ability to provide a broad view.
Plane Mirrors:
- Image Reflection: Plane mirrors produce images that are the same size as the object, and they are upright and virtual.
- Limitations in Distance: While they can show full-length images, they require the viewer to be positioned correctly, and they do not provide the wide-angle view that a convex mirror offers.
Conclusion:
In conclusion, a convex mirror is the optimal choice for viewing a distant tall building because of its ability to provide a wider field of view and maintain the proportions of the image, making it suitable for capturing large objects effectively.

-2 D.

Explanation:
When a glass is placed in a liquid with the same refractive index as glass, the glass will disappear. This phenomenon is known as total internal reflection.

Refraction and Total Internal Reflection:
When light travels from one medium to another, it changes its direction. This change in direction is known as refraction. The amount of bending that occurs depends on the refractive indices of the two mediums. If the refractive indices of the two mediums are the same, there is no bending of light.

In the given scenario, when the glass is placed in a liquid with the same refractive index as glass, the light rays passing through the glass and into the liquid will not bend. As a result, the light rays will continue to travel in a straight line without changing direction.

Total Internal Reflection:
Total internal reflection occurs when a light ray traveling from a medium with a higher refractive index to a medium with a lower refractive index strikes the boundary at an angle greater than the critical angle. In this case, instead of bending, the light ray reflects back into the medium with the higher refractive index.

Disappearance of the Glass:
In the given scenario, since the refractive index of the liquid is equal to that of glass, the critical angle will be 90 degrees. Any light ray that strikes the boundary between the glass and the liquid at an angle greater than 90 degrees will undergo total internal reflection.

When total internal reflection occurs at the boundary between the glass and the liquid, the light rays that were initially traveling through the glass will be reflected back into the glass itself. As a result, no light will be transmitted through the boundary, and the glass will appear to disappear when viewed from outside the liquid.

Hence, the correct answer is option 'B' - Disappear.

Given:
- Focal length of the convex lens, f = 20 cm
- The real image produced by the lens is twice the size of the object.

To find:
The distance of the object from the lens.

Solution:
We can use the lens formula to solve this problem. The lens formula is given by:

1/f = 1/v - 1/u

Where,
- f is the focal length of the lens
- v is the image distance from the lens (positive for real images)
- u is the object distance from the lens (positive for real objects)

Step 1: Find the magnification of the lens.
The magnification (m) is given by the formula:

m = -v/u

Given that the image produced is twice the size of the object, we have:

m = -2

Step 2: Substitute the value of magnification in the lens formula.
We can rewrite the lens formula as:

1/f = 1/v + m/u

Substituting the given values:

1/20 = 1/v + (-2)/u

Simplifying the equation:

1/v = 1/20 + 2/u
1/v = (u + 40)/20u

Step 3: Substitute the value of v in terms of u into the lens formula.
Since the image distance v is twice the object distance u, we have:

v = 2u

Substituting this value in the lens formula:

1/(2u) = (u + 40)/20u

Simplifying the equation:

20u = 2(2u + 40)
20u = 4u + 80
16u = 80
u = 5 cm

Step 4: Convert the object distance from cm to em.
Since the given focal length is in em, we need to convert the object distance to em. 1 cm = 0.1 em, so:

u = 5 cm * 0.1 em/cm
u = 0.5 em

Therefore, the distance of the object from the lens is 0.5 em or 30 cm.

Hence, the correct answer is option 'C' (30 cm).

The Magic Mirror and its Combinations

To understand why the correct answer is option 'A', let's break down the question and the different combinations of mirrors mentioned.

The Child's Observation
According to the child's observation, the mirror reflects his head as bigger, the middle portion of his body as the same size, and his legs as smaller. This indicates that the mirror is distorting the reflection by magnifying the head and reducing the size of the legs.

Now, let's analyze the given combinations of mirrors:

Combination a) Concave, plane, and convex:
- Concave mirror: A concave mirror is curved inward, causing light rays to converge at the focus point. It can produce magnified and virtual images depending on the object's position. In this case, the concave mirror could be responsible for magnifying the reflection of the child's head.
- Plane mirror: A plane mirror has a flat surface and reflects light rays without any distortion. It produces an image that is the same size as the object and appears to be at the same distance behind the mirror. As per the child's observation, the middle portion of his body appears the same size, indicating that there is a plane mirror involved.
- Convex mirror: A convex mirror is curved outward, causing light rays to diverge. It produces a reduced and virtual image. In this case, the convex mirror could be responsible for reducing the reflection of the child's legs.

Combination b) Plane, convex, and concave:
- Plane mirror: As explained earlier, a plane mirror reflects light rays without any distortion, producing an image that is the same size as the object. This matches the child's observation of the middle portion of his body being the same size.
- Convex mirror: Again, a convex mirror would reduce the size of the reflection, which matches the observation of the child's legs being smaller. However, there is no explanation for the magnification of the head in this combination.
- Concave mirror: A concave mirror, when properly positioned, can produce magnified and virtual images. However, in this combination, the concave mirror is not providing an explanation for the magnification of the head.

Combination c) Convex, plane, and concave:
- Convex mirror: As mentioned earlier, a convex mirror would reduce the size of the reflection, which matches the child's observation of the legs being smaller.
- Plane mirror: Once again, a plane mirror reflects light rays without any distortion, producing an image that is the same size as the object. This matches the child's observation of the middle portion of his body being the same size.
- Concave mirror: In this combination, the concave mirror does not provide an explanation for the magnification of the head.

Combination d) Convex, concave, and plane:
- Convex mirror: As mentioned earlier, a convex mirror would reduce the size of the reflection, which matches the child's observation of the legs being smaller.
- Concave mirror: A concave mirror can produce magnified and virtual images. However, in this combination, there is no explanation for the magnification of the head.
- Plane mirror: Once again, a plane mirror reflects light rays without any distortion, producing an image that is the same size as the object. This matches the child's

The given question is related to optics and the formation of images by a convex lens. Let's analyze the given information step by step.

Convex Lens:
A convex lens is a lens curved outward on both sides. It is thicker at the center and thinner at the edges. Convex lenses are also called converging lenses because they converge the incident light rays.

Virtual Image:
A virtual image is formed when the light rays appear to come from a point behind the lens. It cannot be obtained on a screen and is always erect (upright).

Erect Image:
An erect image is an image that is not inverted. It appears in the same orientation as the object.

Magnified Image:
A magnified image is an image that appears larger than the object. It can be larger in size or just appear closer.

Focal Length:
The focal length of a lens is the distance between the lens and the point where parallel light rays converge or appear to diverge from. For a convex lens, the focal length is positive.

Given Information:
The focal length of the convex lens is 10 cm.

Analysis:
Since the image formed is virtual, erect, and magnified, it means that the object is placed between the lens and its focus.

When an object is placed between the lens and its focus, a magnified and erect virtual image is formed on the same side of the lens as the object.

Therefore, the distance of the object from the lens is less than the focal length.

Solution:
The distance of the object from the lens is 5 cm. (Option B)

To summarize, when a virtual, erect, and magnified image is formed by a convex lens of focal length 10 cm, the object distance from the lens is 5 cm.

45 cm

We can use the formula for linear magnification in a convex mirror:

m = -v/u

where m is the linear magnification, v is the image distance, and u is the object distance.

We are given that m = 1/3 and the focal length f = 15 cm. We know that for a convex mirror, the focal length is negative, so f = -15 cm.

We can rearrange the formula to solve for u:

u = -v/m

Substituting in the given values:

u = -(-15)/1/3 = 45 cm

Therefore, the distance of the object from the mirror is 45 cm.