Physics 2016 Jamb Examination

Myopia, or short-sightedness, occurs when the eyeball is too long or the lens is too curved, causing light rays from distant objects to focus in front of the retina rather than directly on it.

To correct this, a diverging or concave lens is used. The concave lens spreads out the incoming parallel light rays before they enter the eye, effectively pushing the focal point further back so that it falls precisely on the retina, allowing for clear distance vision.

The magnetic force (F) acting on a charged particle moving through a magnetic field is given by the formula:\[ F = qvB \sin \theta \]Where \( q \) is the charge, \( v \) is the velocity, \( B \) is the magnetic field strength, and \( \theta \) is the angle between the velocity and the magnetic field. When the particle moves parallel to the field, the angle \( \theta \) is 0°. Since \( \sin 0^{\circ} = 0 \), the magnetic force acting on the particle is zero. With no net force acting to deflect it, the particle continues to move in its original direction according to Newton's First Law, resulting in a straight-line path.

Humidity refers to the amount of water vapour present in the air. When humidity is low, the air is 'dry' and has a high capacity to absorb more moisture. This creates a steep concentration gradient between the surface of the water pool and the surrounding atmosphere, which significantly increases the rate of evaporation. In contrast, on a high-humidity day, the air is already saturated with water vapour, which hinders the escape of molecules from the liquid surface. Therefore, low humidity leads to rapid evaporation.

The acceleration due to gravity (g) follows an inverse-square law relative to the distance from the centre of the Earth. The formula for gravitational acceleration (\( g' \)) at a distance (r) is:\[ g' = \frac{GM}{r^2} \]At the Earth's surface, where the radius is \( R \):\[ g = \frac{GM}{R^2} \]For a satellite at an orbital radius of \( 4R \):\[ g_{sat} = \frac{GM}{(4R)^2} = \frac{GM}{16R^2} \]Substituting \( g = \frac{GM}{R^2} \) into the equation:\[ g_{sat} = \frac{1}{16} \left( \frac{GM}{R^2} \right) = \frac{g}{16} \]Thus, the acceleration of the satellite is one-sixteenth of the acceleration at the Earth's surface.

Light energy can be produced directly from several other forms of energy. Chemical energy can be converted directly into light through chemiluminescence (as seen in glow sticks) or bioluminescence (in fireflies). Electrical energy is directly converted into light in devices like Light Emitting Diodes (LEDs) or through gas discharge in neon tubes. Sound energy, however, does not typically convert 'directly' into light in standard physical processes (sonoluminescence is a highly specialized and rare laboratory phenomenon not usually considered in this context). Therefore, chemical and electrical energy are the primary sources that can be directly transformed into light.

The magnification (m) of a pinhole camera is given by the ratio of the image height (\( h_i \)) to the object height (\( h_o \)), which is also equal to the ratio of the image distance (v) to the object distance (u):\[ m = \frac{h_i}{h_o} = \frac{v}{u} \]From this, the size of the image is:\[ h_i = \frac{v \cdot h_o}{u} \]If the distance between the object and the pinhole (u) is reduced by half (new distance = \( u/2 \)), while the camera length (v) and object size (\( h_o \)) remain constant, the new image height (\( h_i' \)) becomes:\[ h_i' = \frac{v \cdot h_o}{u/2} = 2 \left( \frac{v \cdot h_o}{u} \right) = 2h_i \]Therefore, the size of the image is doubled.

In a plane mirror, the distance from the object to the mirror is equal to the distance from the mirror to the image.
Initially:
Object distance = 15cm
Image distance behind mirror = 15cm
Total distance between object and image = 15 + 15 = 30cm.

After moving the mirror:
The mirror moves 5cm further away, so the new object distance = 15 + 5 = 20cm.
The new image distance behind the mirror will also be 20cm.
The new total distance between the object and the image is:\[ \text{Total Distance} = 20\text{cm (object to mirror)} + 20\text{cm (mirror to image)} = 40\text{cm} \]

Efficiency is defined as the ratio of Mechanical Advantage (MA) to Velocity Ratio (VR). In an ideal machine, efficiency is 1 (or 100%), but in real machines, it is always less than 1 due to energy losses. Friction is a major cause of energy loss in machines, as it converts some of the input work into heat. As friction increases, more effort is required to move the same load, which decreases the Mechanical Advantage (MA). Since Efficiency = MA/VR, a decrease in MA while the VR (which is purely geometric) remains constant results in a decrease in efficiency. Therefore, efficiency decreases with an increase in friction.

A telescope is an optical instrument designed specifically to make distant objects, such as stars, planets, and galaxies, appear much closer and brighter. It achieves this by using a large objective lens or mirror to gather more light than the human eye can alone and then magnifying the image with an eyepiece. While prism binoculars can also be used for stargazing, the primary and more powerful scientific instrument dedicated to this purpose is the telescope. A microscope is used for tiny, nearby objects.

The angular magnification (M) of an astronomical telescope in normal adjustment is given by the ratio of the focal length of the objective lens (\( f_o \)) to the focal length of the eyepiece lens (\( f_e \)).
Given:
Focal length of objective \( f_o = 30 \; \text{cm} \)
Focal length of eyepiece \( f_e = 3 \; \text{cm} \)
Using the formula:\[ M = \frac{f_o}{f_e} \]\[ M = \frac{30}{3} = 10 \]The telescope provides an angular magnification of 10, meaning distant objects will appear ten times larger than when viewed with the naked eye.