Step 2: Very Short Questions
a. Long-sightedness is represented by option A in the table because it occurs when the ciliary muscles cannot contract enough to make the eye lens curve sufficiently for near vision.
b. The defect of vision A, which is corrected by raising the middle of the cornea to make it more curved and increase its converging power, is long-sightedness or hypermetropia.
c. If Junu suffers from a nail scratch on her cornea, she will likely experience blurred vision because the cornea’s ability to act as a clear window for refracting light into the eye is impaired.
d. One common application for the arrangement where an object is placed between F and 2F of a convex lens to produce a magnified real image is a slide projector or film projector.
e. The statement “the power of a lens is 1 dioptre” means that the lens has a focal length of exactly one meter.
f. To obtain an image that is diminished, inverted, and real, the object should be placed beyond the center of curvature or 2F in front of a convex lens.
g. Rhodopsin is a light-sensitive pigment found in the rod cells of the retina that is primarily composed of protein and helps with vision in dim light.
h. If a protein crystal accumulates in the lens of the eye and forms a grey, cloudy spot, the condition is known as a cataract.
i. Laser surgery used to make the middle part of the cornea flatter is a treatment for short-sightedness or myopia.
Step 3: Short Questions
a. Differences between Convex Lens and Concave Lens
Convex Lens:
- It is thicker in the middle and thinner at the edges.
- It converges parallel rays of light to a point, acting as a converging lens.
- It has a positive focal length and power.
- It can form both real and virtual images depending on object position.
- It is used to correct long-sightedness (hypermetropia).
- It is used in magnifying glasses, cameras, and projectors.
- When held in sunlight, it can focus light to a point and burn paper.
- Concave Lens:
- It is thinner in the middle and thicker at the edges.
- It diverges parallel rays of light, acting as a diverging lens.
- It has a negative focal length and power.
- It always forms a virtual, erect, and diminished image.
- It is used to correct short-sightedness (myopia).
- It is used in peepholes, some telescopes, and eyeglasses for nearsighted people.
- When held in sunlight, it spreads out the light rays and cannot burn paper.
b. When an object is placed between the optical centre and the focus of a convex lens, the features of the image are as follows:
∙ The image is virtual and cannot be caught on a screen.
∙ The image is erect or upright.
∙ The image is highly enlarged or magnified compared to the object.
∙ The image is formed on the same side of the lens as the object.
c. Since the focal length is 2 cm and the candle is at 4 cm, the object is placed exactly at 2F. The light rays from the candle pass through the convex lens and converge at 2F on the opposite side, forming a real, inverted image of the same size.
d. To represent the defective eye (myopia), draw parallel rays entering the eye and meeting at a point in front of the retina rather than on it.
e. A corneal injury is any damage, such as a scratch or abrasion, to the clear, protective outer layer of the eye known as the cornea. When a sharp tool scratches the cornea, it causes a corneal abrasion which allows liquid to build up at the site, resulting in blurred vision. Therefore, this injury can lead to severe visual impairment, and if the cornea becomes conical as a result, the condition is referred to as keratoconus.
f. Night blindness is a vision defect where a person can see clearly during the day but has poor vision at night or in dim light. Yugal is likely suffering from this condition because his diet lacks fruits and vegetables, leading to a deficiency in Vitamin A which is essential for the rod cells in the retina to function properly. In conclusion, he should begin eating Vitamin A-rich foods such as carrots, sweet potatoes, and green leafy vegetables to recover his vision.
g. Accommodation is the ability of the eye lens to adjust its focal length using ciliary muscles to focus on objects at various distances. When Manish looks far away from the window, his ciliary muscles relax, making the eye lens thinner and increasing its focal length so distant objects appear sharp on the retina. As he looks back at the book, the ciliary muscles contract, which makes the eye lens thicker and decreases the focal length to clearly see the nearby text. This process happens instantly and automatically to ensure that light rays are always converged onto the light-sensitive retina. Thus, the ciliary muscles act as a self-adjusting mechanism that provides immediate visual clarity for both near and far distances.
h. In the ray diagram where the object is beyond 2F, the ray parallel to the principal axis passes through the focus (F) after refraction, and the ray through the optical centre (C) goes straight. The rays meet between F and 2F on the other side. The nature of the image is real, inverted, and diminished.
Step 4: Long Questions
a. Based on the study of the hand lens:
∙ i. A convex lens is used for book reading because it can produce a magnified virtual image.
∙ ii. The object must be kept between the optical centre (O) and the principal focus (F).
∙ iii. Draw a ray diagram where diverging rays refracted by the convex lens are traced back to form an enlarged, virtual, and erect image on the same side.
b. To produce a parallel beam of light, the source of light (bulb) must be placed exactly at the principal focus (F) of the convex lens.
c. Sharmila is suffering from long-sightedness or hypermetropia because she can read distant text but not nearby books. The causes of this defect are the shortening of the eyeball or an increase in the focal length of the eye lens due to it being too thin. To correct this, she wears spectacles with convex lenses that converge light rays before they enter the eye so the image forms correctly on the retina.
d. Regarding the work of Dr. Sanduk Ruit:
Dr. Sanduk Ruit is a renowned Nepali ophthalmologist who has restored sight to over 180,000 people across Asia and Africa through his innovative small-incision cataract surgery technique. The intraocular lens is an inexpensive artificial lens that can be produced for as little as $3 each, compared to the previous cost of $100-150 per lens. During cataract surgery, the natural crystalline lens of the eye, which has become cloudy, is replaced by this artificial intraocular lens.
Dr. Ruit developed a revolutionary sutureless surgical technique that can be performed in as little as five to ten minutes through tiny incisions. The procedure involves removing the cloudy cataract through small incisions without stitches and replacing it with a low-cost artificial lens. He founded the Tilganga Institute of Ophthalmology in Kathmandu in 1994, which manufactures these affordable intraocular lenses and has made them available to over 60 countries. The institute performs thousands of surgeries weekly, with many procedures provided free to those unable to pay.
To prevent cataracts, young people should avoid excessive exposure to UV rays by wearing protective sunglasses, maintain a healthy lifestyle with proper nutrition rich in vitamins A and C, avoid smoking and excessive alcohol consumption, and manage conditions like high blood pressure and diabetes that can increase cataract risk. Regular eye examinations are also important for early detection and treatment.
Step 5: Numerical Problems
Problem 1: Power of Concave Lens
Solution:
Given Data:
∙ Focal length of concave lens, f = -10 cm = -0.1 m
Formula:
P = 1/f
Calculation:
P = 1/(-0.1)
P = -10 D
Answer: The power of the lens is -10 dioptre.
Problem 2: Power of Convex Lens
Solution:
Given Data:
∙ Focal length of convex lens, f = 3 cm = 0.03 m
∙ Object distance, u = 4 cm
Formula:
P = 1/f
Calculation:
P = 1/0.03
P = 33.33 D
Answer: The power of the lens is 33.33 dioptre.
Nature of Image: The image formed is real, inverted, and magnified because the object is between F and 2F.
Problem 3: Focal Length from Power (Solar Beam)
Solution:
Given Data:
∙ Power of convex lens, P = 10 D
Formula:
f = 1/P
Calculation:
f = 1/10
f = 0.1 m
f = 10 cm
Answer: The paper must be kept at 10 cm from the lens.
Problem 4: Focal Length and Type of Lens
Solution:
Given Data:
∙ Power of lens, P = -4.5 D
Formula:
f = 1/P
Calculation:
f = 1/(-4.5)
f = -0.2222 m
f = -22.22 cm
Answer: The focal length is -22.22 cm.
Type of Lens: Concave lens
Defect of Vision: Short-sightedness or Myopia