Refraction, Lenses, and Image Formation

• These notes cover concepts related to refraction, lenses, and image formation, including critical angle, total internal reflection, lens power, magnification, and the sign conventions used in optics

Critical Angle and Total Internal Reflection

• The critical angle for glass is 42°.
• The critical angle is the angle of incidence at which the angle of refraction is 90° when light travels from a denser to a rarer medium.
• Refraction occurs when light enters obliquely from one transparent medium to another, causing a deviation in its path.
• Total internal reflection happens when light travels from a higher to lower optical density medium at an angle greater than the critical angle, reflecting back into the same medium without refraction.

Identifying and Correcting Wrong Statements

• Statement b is incorrect: light velocity is lower in media with higher optical density.
• Statement c is incorrect: glass has a higher optical density than water.
• Refraction arises from differences in the optical density of different media.
• Light velocity in a vacuum is 3 x 10^8 m/s.

Magnification

• When an object is placed at 2F of a convex lens, the magnification of the formed image is 1.

Lens Power and Focal Length

• A lens with a power of -1.25 D is a concave lens.
• Lens power is the reciprocal of its focal length.
• A lens with a power of -1.25 D has a focal length of -20 cm.

Ray Diagrams and Image Formation with Convex Lenses

• When an object is placed in front of a convex lens:
• When the object is placed at 2F, the image is formed at 2F.
• To get a virtual image with a convex lens, place the object between the optic center and the focus.
• Use ray diagrams to find the image position and characteristics.
• For convex lenses, images formed between F and 2F are real and inverted.
• The ray diagram helps determine the image position for an object in front of a lens.

Concave Lenses

• Concave lenses diverge parallel light rays.

Convex Lenses

• With a convex lens of focal length 15cm, to get an image twice the size of the object.
• Object distance is -22.5 cm.
• Image distance is 45 cm.

Real vs. Virtual Images

• Real images are inverted, can be captured on a screen, are formed by actual light ray intersections and have negative magnification.
• Virtual images cannot be captured on a screen and are erect.

Lens Terminology

• The optic center is the center of the lens.
• Focal length is the distance between the optic center and the principal focus.
• The center of curvature is the center of the sphere of which the lens is a part.
• The principal axis is the imaginary line joining the two centers of curvature through the optic center.

Light Ray Diagrams

• Complete diagrams to show how light rays behave when they encounter lenses.
• When light rays fall parallel to the principal axis of a convex lens, they converge at the principal focus.

Light Entering Glass from Air

• Light bends towards the normal when entering glass from air.

Analyzing a Ray Diagram

• In a ray diagram involving refraction:
• PQ is the incident ray.
• QR is the refracted ray.
• The angle of incidence is 30°.
• The angle of refraction is 19°.
• The light ray bends towards the normal during refraction.
• Light bends towards the normal when moving from a rarer to a denser medium.
• Medium B has a higher optical density.
• Light travels slower in a medium with higher optical density.

Lens Power and Diopters

• Lens power is measured in diopters.

Calculating Power

• Power of a convex lens with a focal length of 10cm is +10 D.

Concave Lenses

• Important facts about concave lenses: -Focal length is -10 cm.
• If the object distance is -40 cm, the image distance is -8 cm

Image Formation with a Convex Lens

• For a convex lens with an object at -20 cm forming a virtual image at 100 cm:
• Focal length is +25 cm.
• Power is +4D.

Convex Lens Image Formation

• For convex lenses, an object placed at 2F forms an image at 2F with a magnification of one.

More on Convex Lenses

• With a convex lens, object distance (u) is -15 cm and image distance (v) is +30 cm.
• Focal length is +10 cm.
• Magnification is -2.

New Cartesian Sign Convention

• Object distance (u) is -40 cm.
• Image distance (v) is +24 cm
• Height of the object (OB) +2 cm
• Height of the Image (IM) is -1 cm

Measuring Distances with the New Cartesian Sign Convention

• Distances measured in the direction of the incident ray are positive.
• The X-axis is the principal axis.

Image Formation with a Concave Lens

• Virtual and erect images are formed between F and O.
• The image is virtual because it cannot be screened.
• With a concave lens, image formed between focus and center is virtual, erect, and diminished.

Lens Types:

• The lens with a real principal focus is a convex lens.

Total Internal Reflection

• Total internal reflection occurs when the angle of incidence is greater than the critical angle, resulting in reflection instead of refraction when light travels from water to air.

Refractive Index and Speed of Light

• In a medium with a lower refractive index, the speed of light is higher.
• Given refractive indices: A (1.33), B (1.62), C (1.47), D (1.52).
• The correct order is A > C > D > B.
• Speed of light in medium B = 1.85 x 10^8 m/s.

Still More on Lenses

-Object distance u = -12cm

• Image distance v = +6 cm.
• The image is real with f = +4 cm.

Explores refraction, lenses, and image formation, covering critical angle, total internal reflection, lens power, and magnification. Includes discussion and correction of common misconceptions about optical density and light velocity. Focuses on the sign conventions.