Mirrors And Images

To solve the problem, we need to understand what it means when the magnification of an image is equal to one.

1. Understanding Magnification:
Magnification (M) is defined as the ratio of the height of the image (h_i) to the height of the object (h_o):

2. If Magnification = 1:
This means:

So, the image is of the same size as the object.

Final Answer:
The correct answer is option (C): Image is of the same size as that of object.

To solve this problem, we need to understand the behavior of a light ray when it passes through the center of curvature of a concave mirror.

1. Center of Curvature Concept:
The center of curvature (C) is the center of the sphere from which the mirror is a part. Any ray passing through the center of curvature of a concave mirror hits the mirror perpendicularly (i.e., along the radius).

2. Law of Reflection:
According to the law of reflection, when a light ray strikes a surface perpendicularly, it reflects back along the same path. This means the ray retraces its path.

3. Evaluating the Options:
(A) Through focus (F) – Incorrect (rays parallel to the principal axis pass through focus after reflection)
(B) Through centre of curvature (C) – Incorrect as a reflected ray cannot newly pass through C, it just retraces if incident from C
(C) Retraces the path – Correct ✅
(D Through any point – Incorrect

Final Answer:
The correct option is (C) Retraces the path.

To solve the problem, we need to determine the correct definition of the focal plane of a spherical mirror.

1. Understanding the Focal Plane:
The focal plane of a spherical mirror is defined as the plane that passes through the focus (F) and is perpendicular to the principal axis.

2. Evaluate the Given Options:
- Option (A): Line joining P and F – This is the principal axis, not the focal plane.
- Option (B): Plane perpendicular to the principal axis at focus (F) – This is the correct definition of the focal plane.
- Option (C): Plane perpendicular at centre of curvature – This is not the definition of the focal plane.
- Option (D): Plane parallel to the principal axis – Also incorrect.

Final Answer:
The correct answer is option (B): Plane perpendicular to the principal axis at focus (F).

To solve this problem, we need to understand the behavior of parallel rays incident on a convex lens at an angle to the principal axis.

1. Behavior of Parallel Rays in Convex Lens:
In a convex lens, parallel rays that are incident along the principal axis converge at the principal focus on the opposite side.

2. Inclined Parallel Rays:
When rays are parallel but inclined (at 15° in this case) to the principal axis, they do not converge at the principal focus directly. Instead, they converge at a point on the focal plane — the plane that is perpendicular to the principal axis and passes through the focus.

3. Evaluating the Options:
(A) Converge at focus (F) – Incorrect (only rays parallel to principal axis do this)
(B) Diverge from focus (F) – Incorrect (diverging happens in concave lenses)
(C) Converge to a point on focal plane – Correct ✅
(D) Diverge from a point on focal plane – Incorrect

Final Answer:
The correct option is (C) Converge to a point on focal plane.

To solve this problem, we need to understand how to draw the normal to a curved surface (such as a mirror or lens) at a given point on its surface.

1. Understanding the Normal to a Curved Surface:
The normal at any point on a curved mirror (concave or convex) is defined as the line that passes through that point and the centre of curvature (C).

2. Why Centre of Curvature?
The centre of curvature is the center of the sphere from which the mirror surface is a part. The radius of this sphere always lies normal (perpendicular) to the surface at any point on the mirror. So, joining the point on the mirror to the centre of curvature gives the correct normal.

3. Evaluating Given Options:

• (A) Focus (F) – Incorrect; it's not used for finding the normal.
• (B) Pole (P) – Incorrect; the normal does not necessarily pass through the pole.
• (C) Centre of curvature (C) – Correct; normal is along the line joining the point and C.
• (D) Any point on principal axis – Incorrect; arbitrary points are not used for normal construction.

Final Answer:
The correct answer is (C) Centre of curvature (C).

To solve the problem, we need to identify which type of mirror is used by dentists to examine the teeth of patients.

1. Understanding Mirror Properties:
- Concave mirror: Forms enlarged, erect images when the object is close. This helps dentists see a magnified view of teeth and gums.
- Convex mirror: Always forms diminished, virtual images. Used in vehicles for a wider field of view.
- Plane mirror: Forms images of the same size as the object, not magnified.
- None of the above: Incorrect since concave mirrors are indeed used.

2. Reason Dentists Use Concave Mirrors:
Concave mirrors focus light and magnify the image, making it easier for dentists to see small details inside the mouth.

Final Answer:
The correct mirror used is the Concave mirror (Option A).

To solve the problem, we need to identify the part of the eye that helps the eye-lens change its focal length.

1. Understanding the Function of the Eye-Lens:
The eye-lens changes its focal length to focus light from objects at various distances onto the retina. This ability is known as **accommodation**.

2. Role of Ciliary Muscles:
Ciliary muscles are responsible for changing the shape of the eye-lens. By contracting or relaxing, they make the lens thicker or thinner, thereby changing its focal length.

3. Evaluating the Options:
- (A) Aqueous humor: A fluid that maintains pressure, not involved in lens adjustment.
- (B) Cornea: Helps in focusing light but not in changing focal length.
- (C) Ciliary muscle: Correct answer – controls the lens shape.
- (D) Pupil: Regulates the amount of light entering the eye, not the lens shape.

Final Answer:
The correct answer is option (C): Ciliary muscle.

To solve the problem, we need to determine the minimum distance at which an object should be placed from the pole of a concave mirror to obtain a real image.

1. Real Image Formation in a Concave Mirror:
In a concave mirror, a real image is formed when the object is placed beyond the focal point (i.e., at a distance greater than the focal length). The real image is formed on the opposite side of the object, and its size and position depend on the object’s distance from the mirror.

2. Minimum Object Distance for Real Image:
For the minimum object distance to obtain a real image, the object must be placed at a distance greater than the focal length, but the image formed will be at the focus (F). Therefore, the minimum distance of the object from the pole to obtain a real image is the focal length, .

Final Answer:
The minimum distance of an object from the pole to obtain a real image in case of a concave mirror is .

To solve the problem, we need to identify which type of mirror is used by dentists to examine the teeth of patients.

1. Understanding Mirror Properties:
- Concave mirror: Forms enlarged, erect images when the object is close. This helps dentists see a magnified view of teeth and gums.
- Convex mirror: Always forms diminished, virtual images. Used in vehicles for a wider field of view.
- Plane mirror: Forms images of the same size as the object, not magnified.
- None of the above: Incorrect since concave mirrors are indeed used.

2. Reason Dentists Use Concave Mirrors:
Concave mirrors focus light and magnify the image, making it easier for dentists to see small details inside the mouth.

Final Answer:
The correct mirror used is the Concave mirror (Option A).

To solve the problem, we need to identify which type of mirror can produce a magnification greater than 1.

1. Understanding Magnification:
Magnification (M) is the ratio of the height of the image to the height of the object. A magnification greater than 1 means the image is larger than the object.

2. Behavior of Different Mirrors:
- A plane mirror always forms an image of the same size, so its magnification is exactly 1.
- A convex mirror always forms diminished (smaller) images, so its magnification is always less than 1.
- A concave mirror can produce magnification greater than 1 when the object is placed between the pole and the focus, forming a virtual, erect, and enlarged image.

3. Conclusion:
Only a concave mirror can produce an image with magnification greater than 1.

Final Answer:
The mirror is a Concave mirror.

To solve the problem, we need to identify the position of the object for which a concave mirror forms a virtual image.

1. Properties of a Concave Mirror:
A concave mirror usually forms real and inverted images, but under certain conditions, it forms a virtual image.
This occurs only when the object is placed very close to the mirror.

2. Condition for Virtual Image Formation:
A concave mirror forms a virtual, erect, and magnified image when the object is placed between the pole (P) and the focus (F).

Final Answer:
A virtual image is formed when the object is placed between the pole (P) and F.

To solve the problem, we need to identify which optical device always produces a diminished and virtual image regardless of the object position.

1. Understanding Image Formation by Lenses:
- A convex lens (converging lens) can form both real and virtual images depending on the object's position. It does not always produce a diminished image.
- A plano-convex lens behaves similarly to a convex lens and can produce magnified or diminished images.
- A concave mirror (converging mirror) can form real, inverted images and virtual, erect images depending on object placement.

2. Concave Lens Behavior:
A concave lens (diverging lens) always forms:
- A virtual image (cannot be projected on a screen)
- A diminished image (smaller than the object)
- An erect image (upright)
This behavior remains the same regardless of the object distance from the lens.

Final Answer:
The lens that always gives a diminished and virtual image is the

Step 1: Identify the Lens Maker’s Formula
The lens maker’s formula for a lens in air is:

where is the focal length, , , and .

Step 2: Apply the Sign Convention for a Double Concave Lens
For a double concave lens:
- The first surface is concave, so (negative as the center of curvature is to the left).
- The second surface is convex to the incident light, so (positive as the center of curvature is to the right).

Step 3: Substitute Values into the Formula
- Refractive index term: .
- .
- .
- .
- .
- .

Step 4: Analyze the Result
The focal length is negative, confirming that the lens is diverging, which aligns with the properties of a double concave lens. The magnitude of the focal length is 32 cm, matching option 3 from the given choices: 16 cm, 24 cm, 32 cm, and 48 cm.

Final Answer: The focal length of the double concave lens is 32 cm (Option 2).