UNIVERSITY OF GUYANA FACULTY OF NATURAL SCIENCES DEPART. OF MATH, PHYS & STATS PHY 110 – PHYSICS FOR ENGINEERS LECTURE 11 (THURSDAY, NOVEMBER 10, 2011) 1

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2.17 Measurement of Refractive Index 3

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2.18 Real and Apparent Depth 5

6 Real & Apparent Depth: The refractive index of a material may be determined using the real and apparent depths.

2.19 Thin lenses – Types & Cardinal Points 7 Lenses: Lens, in optical systems, glass or other transparent substance so shaped that it will refract the light from any object and form a real or virtual image of the object. Contact lenses and lenses in eyeglasses correct visual defects. Lenses are also used in the camera microscope, telescope, and other optical instruments. Other imaging systems may be effectively used as lenses in other regions of the electromagnetic spectrum, such as the magnetic lenses in electron microscopes. Microsoft ® Encarta ® 2007.

2.19 Thin lenses – Types & Cardinal Points 8 Convex Lens: A convex lens curves outward; it has a thick center and thinner edges. Light passing through a convex lens is bent inward, or made to converge. This usually causes a real image of the object to form on the opposite side of the lens. The size of the image and the place where it is in focus depends upon the size and position of the object and the focal point (F) of the lens (the place where light rays converge). Microsoft ® Encarta ® 2007.

2.19 Thin lenses – Types & Cardinal Points 9 Convex Lens:

2.19 Thin lenses – Types & Cardinal Points 10 Concave Lens: A diverging, or concave, lens is curved inward, with a thin center and thicker edges. Light passing through a concave lens bends outward, or diverges. Concave lenses produce only virtual images; that is, light rays do not actually come from the virtual image, but the brain perceives the diverging rays as though they do. In this illustration, a diverging lens forms a smaller, upright image just in front of the actual object. Microsoft ® Encarta ® 2007.

2.19 Thin lenses – Types & Cardinal Points 11 Concave Lens:

2.19 Thin lenses – Types & Cardinal Points 12 Cardinal points of Lenses: 1. Optical Centre: This is the middle of the lens. 2. Centre of Curvature C: Centre of the sphere of which the lens is a part. Since light is incident on either sides, a lens has two centres of curvature. 3. Principal Axis: Imaginary line connecting the two centres of curvature of the lens. 4. Focal point F: Point on the principal axis where a parallel beam converges or appears to diverge after refraction.

2.19 Thin lenses – Types & Cardinal Points 13 Cardinal points of Lenses Cont’d: 1. Focal length f: Distance between optical centre and focal point F. 2. Radius of Curvature r: Radius of the sphere of which the mirror is a part.

2.19 Thin lenses – Types & Cardinal Points 14 Cardinal Points: Physics for the IB Diploma by Tim Kirk, pg 164.

2.19 Thin lenses – Types & Cardinal Points 15 Cardinal Points: Physics for the IB Diploma by Tim Kirk, pg 164.

2.20 Sign Convention 16 Real-is-Positive Sign Convention: This convention states that a distance measured to a real object or image is deemed a positive distance conversely a distance measured to a virtual object or image is a negative distance. NB: The focal length of a convex lens is deemed positive given that its focal point is real while for the concave lens it is negative since its focal point is virtual.

2.20 Ray Diagram Construction 17 The nature and location of images produced by both lenses depends on the location of the object from the lenses. Generally, images that are produced may be real or virtual, magnified or diminished, upright or inverted. Information as the nature and size of images produced by lenses may be deduced from ray diagram construction or by calculation using the lens formula. For ray diagram construction, two of the following three rays drawn from the top of the object must intersect to produce the image:

2.20 Ray Diagram Construction Ray 1: Travels parallel to the principal axis and after refraction passes through the focal point or appears to diverge from it. 2. Ray 2: This is a reverse of Ray 1. It passes through the focal point and after refraction travels parallel to the principal axis. 3. Ray 3: It passes through the optical centre un- deviated by suffers lateral displacement.

2.21 Formation of Images – Convex Lens 19 Physics for the IB Diploma by Tim Kirk, pg 165.

2.21 Formation of Images – Convex Lens 20 Physics for the IB Diploma by Tim Kirk, pg 165.

2.21 Formation of Images – Concave Lens 21 Physics for the IB Diploma by Tim Kirk, pg 165.

2.21 Lens Formula 22 Information as to the nature and location of images formed by lenses may be obtained from calculation employing the lens formula used in conjunction with the Real-is-Positive sign convention. Where u, v, f and r represent object distance, image distance, focal length and radius of curvature.

2.21 Lens Formula 23 Magnification m: This is the ratio of image distance to the object distance or height of the image to the height of the object. Where u, and v represent object and image distances.

2.22 Applications 24 Magnifying Glass

2.22 Applications 25 Microscopes: 17 th Century & Scanning Auger.

2.22 Applications 26 Compound Microscope: Physics for the IB Diploma by Tim Kirk, pg 168.

2.22 Applications 27 Refracting Telescope:

2.22 Applications 28 Refracting Telescope: Physics for the IB Diploma by Tim Kirk, pg 168.

2.22 Applications 29 Reflecting Telecscope:

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31 END OF LECTURE