Questions and Answers
Define 1 dioptre of power of a lens.
1 dioptre is the power of a lens whose focal length is 1 metre.
At what distance should the needle be placed in front of the convex lens if the image is equal to the size of the object?
50 cm
Find the power of a concave lens of focal length 2 m.
-0.5 D
Which one of the following materials cannot be used to make a lens? (Select all that apply)
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Where should the object be placed to observe a virtual image larger than the object in a concave mirror? (Select all that apply)
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Where should an object be placed in front of a convex lens to get a real image the size of the object? (Select all that apply)
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A spherical mirror and a thin spherical lens have each a focal length of -15 cm. What are they likely to be? (Select all that apply)
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No matter how far you stand from a mirror, your image appears erect. What type of mirror is likely to be? (Select all that apply)
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Which of the following lenses would you prefer to use while reading small letters found in a dictionary? (Select all that apply)
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Find the range of distance of the object from the concave mirror to obtain an erect image.
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Name the type of mirror used in headlights of a car.
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What happens when half of a convex lens is covered with black paper?
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Find the position, size, and nature of the image formed when an object 5 cm in length is held 25 cm away from a converging lens of focal length 10 cm.
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How far is the object placed from a concave lens of focal length 15 cm when it forms an image 10 cm from the lens?
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Find the position and nature of the image when an object is placed at a distance of 10 cm from a convex mirror of focal length 15 cm.
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What does a magnification of +1 produced by a plane mirror mean?
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Find the position of the image, its nature, and size when an object of length 5.0 cm is placed at a distance of 20 cm in front of a convex mirror of radius of curvature 30 cm.
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How far from a concave mirror should a screen be placed to get a sharp-focused image of an object of size 7.0 cm located 27 cm in front of the mirror of focal length 18 cm?
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Find the focal length of a lens of power -2.0 D. What type of lens is this?
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Find the focal length of a corrective lens prescribed by a doctor with power +1.5 D. Is it diverging or converging?
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Study Notes
Light – Reflection and Refraction
- Visibility of objects depends on light; darkness prevents sight.
- Objects reflect light, which is detected by our eyes, enabling visibility.
- Light travels in straight lines, evidenced by sharp shadows of opaque objects.
- Diffraction occurs when light bends around small objects, indicating light behaves as both a wave and a particle.
- This chapter focuses on reflection and refraction of light, particularly using the principles of ray optics.
Reflection of Light
- Reflection occurs primarily on polished surfaces, such as mirrors.
- Laws of reflection:
- The angle of incidence equals the angle of reflection.
- The incident ray, the normal at the point of incidence, and the reflected ray lie in the same plane.
- Plane mirror images are always virtual, erect, the same size as the object, and laterally inverted.
Spherical Mirrors
- Spherical mirrors can be concave (inward-curving) or convex (outward-curving).
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Terminology:
- The pole (P) is the point on the mirror's surface.
- The center of curvature (C) is outside the mirror's reflecting surface.
- The radius of curvature (R) measures the sphere radius; for small apertures, R = 2f (where f is the focal length).
- The principal axis is a straight line through P and C, normal at P.
Concave Mirrors
- Concave mirrors converge light rays to a single point (focus).
- The focus (F) is located on the principal axis.
- Focal length (f) is the distance from P to F.
- A concave mirror can ignite paper by concentrating sunlight, demonstrating the focus.
Image Formation by Spherical Mirrors
- Image characteristics depend on the object's position relative to P, F, and C:
- Object at infinity: image at F, highly diminished, real, inverted.
- Object beyond C: image between F and C, diminished, real, inverted.
- Object at C: image at C, same size, real, inverted.
- Object between F and C: image beyond C, enlarged, real, inverted.
- Object at F: image at infinity, highly enlarged, real, inverted.
- Object between P and F: image behind the mirror, enlarged, virtual, erect.
Ray Diagrams and Image Representation
- Ray diagrams illustrate image formation by showing light ray paths:
- A parallel ray to the principal axis reflects through F (concave) or appears to diverge from F (convex).
- A ray through F reflects parallel to the principal axis.
- A ray through C reflects back on the same path.
- An obliquely incident ray reflects obeying the laws of reflection.
Summary of Image Formation
- The nature, position, and size of images formed by concave mirrors depend on object placement.
- Ray diagrams should be created for varying object positions to visualize image characteristics effectively.### Concave Mirrors
- Commonly used in torches, searchlights, and vehicle headlights for powerful parallel beams of light.
- Shaving mirrors provide an enlarged view of the face for precision.
- Dentists utilize concave mirrors to examine larger images of patients' teeth.
- Solar furnaces employ large concave mirrors to focus sunlight for heat generation.
Convex Mirrors
- Produce virtual, erect, and diminished images regardless of the object's distance from the mirror.
- Images formed when the object is at infinity appear at focus F, regarded as point-sized.
- When the object is between infinity and the pole P of the mirror, the image is located between points P and F, still virtual and erect.
Results from Image Formation by Convex Mirrors
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Object at Infinity:
- Image at focus F, highly diminished and virtual.
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Object Between Infinity and Focus:
- Image located behind the mirror, diminished, and virtual.
Observations with Different Mirrors
- Plane mirrors may not show the full image of a large object.
- Concave mirrors and convex mirrors also vary in full-length image visibility based on the object distance.
Uses of Convex Mirrors
- Act as rear-view mirrors in vehicles, enhancing safety by providing a wider field of view.
- Erect images assist drivers in monitoring traffic, while the curved shape minimizes blind spots.
Sign Convention for Reflection
- New Cartesian Sign Convention is used for spherical mirrors.
- Pole (P) is the origin; distances measured from the pole:
- Positive to the right (x-axis) and above the principal axis (y-axis).
- Negative to the left (x-axis) and below the principal axis (y-axis).
Mirror Formula and Magnification
- The relationship between object distance (u), image distance (v), and focal length (f) is represented by the mirror formula:
- ( \frac{1}{f} = \frac{1}{v} + \frac{1}{u} )
- Magnification (m) reflects the comparative height ratio of image to object:
- ( m = \frac{h'}{h} )
- It can also be calculated using distances: ( m = -\frac{v}{u} ).
Example Calculations
- Convex mirror with radius of curvature 3.00 m shows virtual image at 1.15 m behind the mirror.
- Concave mirror produces an inverted image at 37.5 cm with enlarged size based on object distance from the mirror.
Refraction of Light
- Refraction occurs when light passes from one medium to another, bending its path.
- Observations include the apparent displacement of objects under water or through glass slabs.
Laws of Refraction
- Incident, refracted rays, and the normal lie in the same plane.
- Snell’s Law relates the sine of angles of incidence and refraction, providing a constant for specific media:
- ( \frac{\sin i}{\sin r} = constant ) (refractive index).
Importance of Refractive Index
- Represents how the speed of light changes across different materials and quantifies the extent of bending during refraction.### Speed of Light in Different Media
- Light travels fastest in a vacuum at 3×10^8 m/s, with speed slightly reduced in air.
- The speed of light significantly decreases in denser materials like glass and water.
- The refractive index (n) compares the speed of light in two media: n_21 = v1/v2, where v1 is the speed in medium 1 and v2 is the speed in medium 2.
- Absolute refractive index of a medium (n_m) is defined as: n_m = c/v, where c is the speed of light in air.
Refractive Index Values
- Water has a refractive index (n_w) of 1.33, indicating light travels slower in water than in air.
- Crown glass has a refractive index (n_g) of 1.52.
- Examples of refractive indices from Table 9.3 include:
- Air: 1.0003
- Ice: 1.31
- Kerosene: 1.44
- Diamond: 2.42
- Optical density is not synonymous with mass density; a medium can be optically denser without being heavier.
Optical Density
- Optically denser media have higher refractive indices.
- Light travels faster in rarer media; it bends towards the normal when moving from rarer to denser media and bends away from the normal when moving from denser to rarer media.
Lenses
- Lenses are transparent materials with spherical surfaces that refract light.
- A convex lens (converging) is thicker in the middle and focuses light rays to a point.
- A concave lens (diverging) is thicker at the edges and appears to diverge light rays.
Principal Focus and Focal Length
- The principal focus of a convex lens is where parallel rays converge, while for a concave lens, it’s where rays appear to diverge.
- Focal length (f) is the distance from the optical center to the principal focus.
Image Formation by Lenses
- Lenses form images by refracting light based on the object’s position.
- Image characteristics vary by object distance from the lens, such as being real/inverted or virtual/erect.
Image Formation with Convex Lens
- Convex lens image formation varies according to object distance with characteristics summarized as follows:
- At infinity: Image at focus F2 (highly diminished, real, inverted).
- Beyond 2F1: Image between F2 and 2F2 (diminished, real, inverted).
- At 2F1: Image at 2F2 (same size, real, inverted).
- Between F1 and 2F1: Image beyond 2F2 (enlarged, real, inverted).
- At focus F1: Image at infinity (highly enlarged, real, inverted).
- Between F1 and O: Image on the same side (enlarged, virtual, erect).
Image Formation with Concave Lens
- Concave lenses consistently create virtual, erect, and diminished images regardless of object placement.
Ray Diagrams for Lenses
- Ray diagrams illustrate light behavior through lenses:
- Rays parallel to the principal axis converge at principal focus for a convex lens.
- Diverging rays from the principal focus appear parallel in a concave lens.
- Rays passing through the optical center continue without deviation.
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Description
This quiz covers the concepts of light, reflection, and refraction. It explores how light makes objects visible and the role of sunlight during the day.
