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A person suffers from hypermetropia (long sight) - AQA - A-Level Physics - Question 1 - 2017 - Paper 5
Question 1
A person suffers from hypermetropia (long sight). Use of a spectacle lens of power +2.0D allows the person to just see clearly an object placed 24 cm away from the e... show full transcript
Worked Solution & Example Answer:A person suffers from hypermetropia (long sight) - AQA - A-Level Physics - Question 1 - 2017 - Paper 5
Step 1
Explain why the unaided defective eye cannot form a clearly focused image of the object placed 24 cm from the eye.
Answer
The unaided eye of a person with hypermetropia cannot focus light efficiently on the retina. This is due to the eye's lens being unable to accommodate enough power to converge the light rays from the nearby object, which in this case is placed 24 cm away. The rays coming from the object are too divergent for the eye to focus them properly without the aid of a corrective lens.
Step 2
Calculate the distance of the image formed from the spectacle lens. Give your answer to a suitable number of significant figures.
Answer
To calculate the image distance (v), we use the lens formula:
rac{1}{f} = rac{1}{u} + rac{1}{v}
Where:
- is the focal length of the lens, which can be calculated from the power () using the formula:
f = rac{1}{P} = rac{1}{2.0} = 0.5 meters or 50 cm. - is the object distance, which is -24 cm (the negative sign indicates that it is on the same side as the incoming light).
Plugging in the values:
rac{1}{0.5} = rac{1}{-24} + rac{1}{v}
Solving for gives:
ightarrow v = 0.46 ext{ cm}$$ Thus, the distance of the image formed from the spectacle lens is approximately 0.46 cm.Step 3
Step 4
Draw a ray diagram to show how this spectacle lens forms an image of the object placed 24 cm from the spectacles lens.
Answer
A ray diagram illustrating this phenomenon should include the following elements:
- Two rays from the object.
- One ray parallel to the principal axis that passes through the focal point after refraction.
- Another ray passing through the center of the lens.
- Label the object, the image formed, and the principal focus of the lens.
- Ensure that the diagram is clear, though sizing is not essential.